Proceedings of the Worldwide Music Conference 2021: Volume 2 (Current Research in Systematic Musicology, 9) 3030858855, 9783030858858

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Current Research in Systematic Musicology

Ildar D. Khannanov Roman Ruditsa   Editors

Proceedings of the Worldwide Music Conference 2021 Volume 2

Current Research in Systematic Musicology Volume 9

Series Editors Rolf Bader, Musikwissenschaftliches Institut, Universität Hamburg, Hamburg, Germany Marc Leman, University of Ghent, Ghent, Belgium Rolf-Inge Godoy, Blindern, University of Oslo, Oslo, Norway

The series covers recent research, hot topics, and trends in Systematic Musicology. Following the highly interdisciplinary nature of the field, the publications connect different views upon musical topics and problems with the field’s multiple methodology, theoretical background, and models. It fuses experimental findings, computational models, psychological and neurocognitive research, and ethnic and urban field work into an understanding of music and its features. It also supports a pro-active view on the field, suggesting hard- and software solutions, new musical instruments and instrument controls, content systems, or patents in the field of music. Its aim is to proceed in the over 100 years international and interdisciplinary tradition of Systematic Musicology by presenting current research and new ideas next to review papers and conceptual outlooks. It is open for thematic volumes, monographs, and conference proceedings. The series therefore covers the core of Systematic Musicology, - Musical Acoustics, which covers the whole range of instrument building and improvement, Musical Signal Processing and Music Information Retrieval, models of acoustical systems, Sound and Studio Production, Room Acoustics, Soundscapes and Sound Design, Music Production software, and all aspects of music tone production. It also covers applications like the design of synthesizers, tone, rhythm, or timbre models based on sound, gaming, or streaming and distribution of music via global networks. • Music Psychology, both in its psychoacoustic and neurocognitive as well as in its performance and action sense, which also includes musical gesture research, models and findings in music therapy, forensic music psychology as used in legal cases, neurocognitive modeling and experimental investigations of the auditory pathway, or synaesthetic and multimodal perception. It also covers ideas and basic concepts of perception and music psychology and global models of music and action. • Music Ethnology in terms of Comparative Musicology, as the search for universals in music by comparing the music of ethnic groups and social structures, including endemic music all over the world, popular music as distributed via global media, art music of ethnic groups, or ethnographic findings in modern urban spaces. Furthermore, the series covers all neighbouring topics of Systematic Musicology.

More information about this series at http://www.springer.com/series/11684

Ildar D. Khannanov Roman Ruditsa •

Editors

Proceedings of the Worldwide Music Conference 2021 Volume 2

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Editors Ildar D. Khannanov Peabody Institute Johns Hopkins University Baltimore, MD, USA

Roman Ruditsa St. Petersburg Union of Composers St. Petersburg, Russia

ISSN 2196-6966 ISSN 2196-6974 (electronic) Current Research in Systematic Musicology ISBN 978-3-030-85885-8 ISBN 978-3-030-85886-5 (eBook) https://doi.org/10.1007/978-3-030-85886-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021, corrected publication 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The opening chapter, “Relative Musical Pitch in Formal Definition” by Roman Ruditsa, returns to the centuries-old and cutting-edge mathematical description of tones and their structural relationships. In comparison with current Western approaches (say, Dmitri Tymozcko in the USA or Tomas Noll in Germany), “Relative Musical Pitch” reveals deep connections to Russian tradition in both mathematics and music theory. There is a link to Boleslav Yavorski’s idea of conjugation (Russ. coпpяжeниe) and Tatiana Bershadskaya’s definitions of interval and mode (Russ. lad). The formidable breadth of approach allows for the application of Ruditsa’s concept to any music, tonal, atonal and that which has not been written yet. The chapter “The Conceptual Structure of Music: Congruence, Modularity, and the Language of Musical Thought” by Trevor Rawbone capitalizes on previously published research. As such, it offers proved and solid concepts that lie on the border several fields of knowledge. The idea of language of musical thought is as all-embracing as it is precise and rigorous. The author adds several others to the cluster: congruence and modularity harmonize with the main idea, that of LMT. This study presents an exemplary case of interdisciplinarity, in which the most abstract general scientific concepts contrast with but do not encroach upon purely musical ideas. The chapter “To the Question of the Possibility of Identifying the Psychophysiological Signs of “Ethnic Hearing” as Differential Perception of “Native” and “Alien” Music” by Alla V. Toropova and Irina N. Simakova offers a rich perspective on the effects of music on the psychophysiological functions. It stands out among other papers that deal with music and medicine; a 100-unit bibliography and ultimate rigor of definitions are combined with the profound understanding of music and its cultural backgrounds. In particular, the authors address the issue of alien vs. native music, something that had never been discussed in neurobiological terms. It also offers an interesting direction in properly musicological studies, in both historic and analytical subfields.

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This volume of Worldwide Music Conference proceedings would be incomplete without the research in evolutionary musicology. The chapter “Correlations between Musical and Biological Variation in Derivative Analysis” by Carlos Almada presents an elegant and profoundly musical discourse on variation. Indeed, in music theory this term is taken for granted: Almada suggests placing it in the context of evolutionary research. The paper begins with an homage to Darwin and deftly summarizes a wide spectrum of approaches to this category, as important as the idea of development itself. The next chapter “Thinking/Feeling Musical Narrative” by Vincent Meelberg explores one of the most elusive terms, the narrative. Rather appealing is the rich personal experience of the author in composition and improvisation. He brings in Lyotard, Almén, Sternberg and Gershon in one context. All the previous approaches to this topic are addressed here; the author offers his own view that relies on the ideas of event, affect and, ultimately, sonic thinking. Needless to say how important is musical narrative as a kind of supporting alternative to the more commonly used categories of form and harmonic progression. Daniil Shutko presents a study that is an homage to his professor, late Dr. Tatiana Bershadskaya of St. Petersburg [Leningrad] Conservatory. The text is based upon solid research, a tradition that involves several generations of theorists. The topic belongs to the core of music theory. The idea of lad—Russian indigenous term that covers a cluster of meanings—and melodic aspect of harmony are the gems of Leningrad school. They are presented for the first time in the West. Another mathematical approach to musical interval is suggested in the paper “What are musical intervals? A question recharged via an algebraic theory of measurement” by Celina Richter and Stefan E. Schmidt. This paper is concise and down to the point: It offers a system of algebraic representation and measurement of interval as a monoid. There are topics in musicology and in music theory that seem to be marginal but prove to be essential. Such are, for example, treatises on laughter and humor, common in both early history of music and current musicology. However, perhaps the most unusual topic that is proposed for this collection and exhaustively laid out in scholarly fashion is the chapter “About the Apollonian and the Dionysian: Dialogues between Music and Wine in the Spanish Social Context” by Diego Pérez-Fuertes, Emma Juaneda-Ayensa and Cristina Olarte-Pascual. Its jovial tone cannot hide the seriousness of the problematics: the effect of pandemic of COVID-19 on music perception, in particular, and on the quality of life, in general. The connection of music and festivity has been vital for all recorded human history. The chapter can be of interest for those who engage in musical sociology, theory of musical emotion and many other interdisciplinary fields. Ildar Khannanov Roman Ruditsa The original version of the book was revised: The book volume number has been changed to 9. The correction to the book is available at https://doi.org/10.1007/978-3-030-85886-5_9

Contents

Mathematics of Pitch and Interval Relative Musical Pitch in Formal Definition . . . . . . . . . . . . . . . . . . . . . . Roman Ruditsa What Are Musical Intervals? A Question Recharged via an Algebraic Theory of Measurement . . . . . . . . . . . . . . . . . . . . . . . Celina Richter and Stefan E. Schmidt

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Language and Narrative Thinking/Feeling Musical Narrative . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vincent Meelberg The Conceptual Structure of Music: Congruence, Modularity, and the Language of Musical Thought . . . . . . . . . . . . . . . . . . . . . . . . . . Trevor Rawbone

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Evolution and Perception Correlations Between Musical and Biological Variation in Derivative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Carlos Almada To the Question of the Possibility of Identifying the Psychophysiological Signs of “Ethnic Hearing” as Differential Perception of “Native” and “Alien” Music . . . . . . . . . . . Alla V. Toropova and Irina N. Simakova The Musical-Theoretical Concept of Tatiana Sergeyevna Bershadskaya . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Daniil Shutko

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Sociology About the Apollonian and the Dionysian: Dialogues Between Music and Wine in the Spanish Social Context . . . . . . . . . . . . . . . . . . . Diego Pérez-Fuertes, Emma Juaneda-Ayensa, and Cristina Olarte-Pascual

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Correction to: Proceedings of the Worldwide Music Conference 2021 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ildar D. Khannanov and Roman Ruditsa

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Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Mathematics of Pitch and Interval

Relative Musical Pitch in Formal Definition Roman Ruditsa(B) St. Petersburg Union of Composers, St. Petersburg, Russia [email protected]

Abstract. This research is dedicated to the category of relative musical pitch and its objects such as tones, intervals, interval structures, and systems. Objects of relative pitch are considered as necessarily existing in their systemic unity. The study introduces the concept of structural-pitch organization (SPO), an object that signifies the unity of objects of relative pitch. SPO is defined as an aggregate of representatives of all possible classes of objects of relative pitch, taken together with the system of relations between them. Being associated with both acoustic and psycho-physiological phenomena, the SPO and its components are abstract, mental objects. The study is devoted to the abstract-logical aspect of relative pitch, considering it is strictly distinguished from the “natural” aspect. The SPO is examined as an attribute of a special type of so-called structural-pitch thinking. The aggregate of relations between SPO objects represents the specific principles of such thinking, that is, those in which it is independent of either natural factors or other types of mental activity (types of thinking and expression). The study provides formal definitions of the SPO objects. These definitions are derived by means of set theory. The study offers a formal definition of the content of the SPO (that is, the scheme of the content of structural-pitch thinking). I demonstrate that there exists not an SPO in general, but a class of SPOs, whose representatives differ in content and characterize the pitch thinking of individuals and communities in different cultures and epochs. Keywords: Music theory · Musical thinking · Music and mathematics · Musical set theory · Musical pitch · Interval · Tone

1 Introduction 1.1 Subject of the Study The subject of the study is objects of relative musical pitch, such as tones, intervals, interval structures, and systems. We consider the objects of relative pitch as necessarily existing in their inseparable unity. This unity is expressed in the object we call structuralpitch organization and define it as an aggregate of objects of relative pitch representing classes from a certain set of classes together with the system of relations existing between these objects. Furthermore, we use SPO instead of the term structural-pitch organization. As the objects of relative pitch under study are considered by us within the SPO, we will call them objects of SPO. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. D. Khannanov and R. Ruditsa (Eds.): WWMC 2021, CRSM 9, pp. 3–17, 2021. https://doi.org/10.1007/978-3-030-85886-5_1

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1.2 Clarifications There is no SPO in general; in other words, there is no unique SPO encompassing all existing objects of relative pitch. All classes of these objects are necessarily represented in the SPO; however, these classes can have different sets of representatives. In other words, there is a class of structural-pitch organizations, the representatives of which differ in the sets of objects included in them. The properties common to all structuralpitch organizations are the set of classes of their objects and the system of relations between these objects. The relations between objects (sets of objects) from different classes of SPO objects are primarily the following: the relation between A and B, from which the existence of A logically precedes the existence of B; the relation between C and D, from which the existence of C entails the existence of D; the relation between E and F, from which properties of E determine properties of F. (Meanwhile some letter may denote an aggregate of sets of objects from different classes). The term “musical” is used by us in the most traditional sense and at the same time purely conditionally. There are numerous phenomena called musical, in which there are no abovementioned objects, and even the independent existence of pitch [8, 15]. We do not intend to contribute to the resolution of the question of the expediency of naming certain phenomena “musical” [3]. The word “musical” in our text could be harmlessly replaced with a semantically neutral sign, for example, a letter. 1.3 Aspects of Consideration of the Objects Under Study SPO and all its objects are considered by us in the abstract logical aspect, that is, as objects of thought. The SPO objects also have a “natural” aspect, i.e. physical, psychophysiological predetermination. We can assume that objects of SPO in their mental status and SPO as a cognitive structure are influenced by natural factors or even originate from natural objects as a result of abstraction. But even with the latter assumption, if there is the existence of the SPO and its objects in mental status, in this existence they are subject to mental laws (including laws of a logical nature) that operate independently of natural factors. We view the SPO as an attribute of a special form of thinking. Here we mean the following: the question of what musical thinking is in general is obscure, let alone the question of what the thinking is at all. But if we recognize that thinking has or generates abstract objects; that it is characterized by procedures executed on these objects, then the type of mental activity, the attribute of which the SPO is, has the properties of thinking (let this type is conventionally called structural-pitch thinking). Not only natural factors, but also different forms of thinking and expression of not essentially musical (in particular, mathematical, grammatical thinking) influence musical pitch, including the SPO [4]. We assume that these influences, as well as natural factors, define the specific forms of objects of the SPO, but neither their mental specificity not their existence (at least in the mental status). There are such principles of the SPO, which emphasize it as autonomous mental object and therefore separated from forms of thinking outside of the structural-pitch and

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abstracted from natural factors. These principles are the very system of SPO relations (let us call them proper principles of the SPO).1 The system of SPO relations is an “internal logic” of structural-pitch thinking. This word use is metaphorical: we call own principles of SPO the “internal logic” of structuralpitch thinking because they perform in it the same function as logic does in conceptual thinking, and not because they are a fragment of logic as such. SPO is a factor in the formation of musical texts in the structural-pitch aspect. Naturally, the SPO is not the only factor that shapes the text. In the cases where the structural-pitch aspect of the text organization is the SPO in the understanding we have indicated, all aspects of the text organization are clearly separated, and the influence of the factors belonging to them is expressed in indirectly interdependent parameters of the text elements (we are talking about such parameters as pitch, temporal parameter, timbre, dynamic, etc.). However, even in these cases, the aspects of the text organization are in systemic interaction, and some aspect may determine the structure of the text to some extent in some other aspect.2 There are also super-aspectual factors that have a formative effect on the text, acting in several or even in all aspects of text organization. The most important among these factors is a mode.3 Finally, forming factors absolutely outside of musical thinking can influence the musical text. (Examples of that can be all sorts of tone and rhythmic codes and ciphers, using of tones for transmission of words through the names of tones, etc.) In its proper principles, the SPO is independent of any other factors of text organization. We consider exclusively extratextual SPO, that is, such, objects of which do not contain parameters pertaining to any aspects except structural-pitch, and are guaranteed to exist before texts. The principles of the extratextual SPO, manifested in the text, are guaranteed to be independent of other organizing factors. In particular, in our study the SPO is abstracted from the temporal aspect. Strictly speaking, the temporal aspect in relation to the SPO is nothing more than the order of inputs and outputs of tones, which defines their sequence or simultaneity. Accordingly, we do not consider such specific textual objects as simultal (so-called vertical), sequential (in particular, melodic), diagonal tone aggregates. 1 There are conceptions where music is affected by determining influences of non-musical types

of thinking and expression [7]. We do not deny the regularity of these influences (and do not believe that they necessarily contradict the essence of music) [11]. However, we also believe that there are principles in which music is autonomous, encompassing its identity. These include the principles of SPO. 2 For example, if the idea of a certain rhythmic figure exists before the aggregate of tones corresponding to this figure, the temporal aspect way affects in a decisive the pitch structure through setting the number of appearances of tones. 3 Here we should mention the works of Tatiana S. Bershadskaya, devoted to the musical system (understood primarily as a systemic aggregate of aspects of text organization), as well as the general mode theory [1, 2]. In these very works the status of over-aspect factor is revealed— which belongs to the mode—thus demonstrating that the mode is in no case a pitch (in particular, structural-pitch) phenomenon. We should note that the mixing of concepts related to the mode and the pitch structure is often allowed by theorists, including those who have contributed a lot to the separation of these concepts [9].

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1.4 Research Objectives and Methods The objectives of this study are as follows: • identification of all classes of SPO objects in its extratextual status; • provision of accurate definitions; • definition of the relationship between its objects, that is, revealing own principles of the SPO. To do this, we will deduce formal definitions of SPO objects. The definitions form a sequence that is constructed in such a way that all logically necessary SPO objects (not just the most obvious ones listed above) are identified; that objects are strictly different; that prevents inclusion of imaginary objects. Meanwhile, the system of SPO relations is reconstructed as well. Definitions are provided by means of set theory. An object that lacks representatives of at least one of the classes of extratextual SPO objects and lacks some relations inherent to the SPO is not SPO. (Such object is not an attribute of structural-pitch thinking.) Notice: having determined that we are considering only extratextual SPO, we have excluded from consideration some of the own principles of the SPO: the principles of extratextual SPO are proper in any case, however, this does not mean that there are no proper principles of textual SPO.

2 Preliminary (Informal) Overview of Research Objects We will consider the SPO objects, bearing in mind that we aim to deduce formal definitions of these objects, i.e., to define them through their properties and relations that exist between them. 2.1 Tones and Intervals We will accept that the tone is a pitch value. In more detail: we consider tones as objects that have a property to be a value (of other objects), and such values that are called pitch. In relation to absolute pitch, the meaning of this can be expanded as follows: a tone is an abstract object with which we identify material to some degree. Objects are characterized by a pitch—such as sounds or intra-aural images. In absolute pitch a tone exists logically and independently of any objects.4 4 To clarify, first, the tone can be considered as an object originating from physical phenomena

because of sense making of them, however, this possibility is beyond our study. For us it is important that, since the absolute pitch tone exists, then in the act of pitch thinking or perception its presence is not caused logically by the presence of any other objects (including those from which it hypothetically occurs as a result of abstraction). Secondly, it is known (especially from studies of the zonal nature of hearing [10]) that there is no a one-to-one correspondence between absolute pitch tones and physical objects (their frequency parameters, in essence, real numbers). Therefore, determination of absolute pitch tones depends on the context, on the comparison with other objects (in particular, belonging to relative pitch). The above is true for intraaural images as well. However, the dependence of tone determination on other objects does not imply the dependence of existence of the tone on them.

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The SPO is an object of relative pitch. Let us expand the meaning of this expression. The SPO does not contain the objects that, being pitch values (i.e. tones), exist independently of other objects. Relative pitch tone is the value of a certain object in relation to other objects. For the existence of tones in the SPO, objects of two classes are required: the objects, for which or relative to which the tones are determined, belong to the first class, and the objects determining the tones belong to the second one. The objects of the first of these classes are abstract supports of tones. We will call these objects the primary elements of the SPO. Intervals are the objects that determine tones, and the interval determines the tone for some primary element relative to the single primary element. There is a set of intervals in the SPO, the content of which is the basic characteristic of the SPO.5 We will call determined the primary element for which the tone is determined; we will call determining the element relative to which the tone is determined. 2.2 Interval Structures and Interval Systems Among the concepts pertaining to the SPO, the key one is the concept of interval structure. The interval structure can be clearly presented in the form of a graph: graph vertices correspond to the primary elements, the edges (or arcs) correspond to the intervals. However, when considering interval structures, reference to the notion of graph is expedient not only because the graph in this case is a natural demonstration (in this demonstration the graph is no more than a diagram). Taken as an abstraction, the interval structure is a set of objects, one of which is indistinguishable from a graph with known properties (and here we use the concept of the graph in the set theory sense). Interval structure includes a set of primary elements and a set of pairs of elements of this set, for each pair there is a corresponding interval. These two sets form the interval structure graph; the second of them (a set of pairs) will be called the graph relation. The interval determines the pitch value of one of the elements of the pair relative to another element, so the pairs belonging to the graph relation are ordered, and the interval structure graph is directed. In the interval structure, tone can be determined for some element relative to another directly or indirectly. Directly the tone is determined in a pair from the graph relation. But in the general case, it is determined in such a pair for which in the graph of interval structure there exists an oriented path from the determining element to the determined one (or on the opposite, if in the pairs from the graph relation we put arrows from the determined elements to the determining ones)6 . If this path consists of more than one pair from the graph relation, the tone is determined indirectly. The integrity of the interval 5 We should clarify: intervals as SPO objects have a “pitch thinking” nature and do not correlate

with numbers within the SPO. However, a correspondence can be established between them and subsets of a certain set of numbers, the elements of which have acoustic meaning. Thus, the semantics of SPO is determined on the set of numbers. 6 Let the element a be determined, and the element b be determining. Then, there is a sequence of pairs belonging to the graph relation, such that in the first one, a is the determined one, and in the last one, b is the determining one, and for any pair (except for the first one), the determined element is the determining element of the previous pair.

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structure consists in the fact that among its primary elements there is at least one such element relative to which the tone is determined for any other primary element of this structure (directly or indirectly). The graph vertex from which there exists an oriented path to any other vertex is called the central vertex. The interval structure graph is not its only component: its other component is a rule by which intervals from the set of SPO intervals are corresponded by the graph relation elements.7 The interval system is an object of a higher level of abstraction than the interval structure. There may be any number of interval structures, to pairs from graph relations of which intervals are corresponded following the same rule. Such structures represent the same system (in other words: they are its supports). 2.3 Some Technical Concepts Let us introduce the concept of conjugation. Let us take two pairs of primary elements (a, b), (b, c) and assume that the element b in the first of them is the determining one, and in the second the determined one. Two intervals, of which one determines the tone at (a, b) and the other one at (b, c) will be called conjugated and the pair of these intervals a conjugation. (In particular, intervals are conjugated if they correspond to mutually inverse pairs, as in (a, b), (b, a)). Let the graphs of interval structures intersect, and the union of these graphs has a central vertex. Then the systems represented by these structures are called conjugated, the system represented by the union of these structures is called the conjugation of the systems represented by them. Let us introduce the concept of a subsystem. Let the graph of structure B be a subgraph of structure A. The system represented by structure B will be called a subsystem of the system represented by structure A. 2.4 Primary SPO Systems It was stated above that the basic characteristic of the SPO is its set of intervals. This is true, if only because, this set determines all possible interval systems (i.e. sets all possible structures). Of course, the content of the set of these systems depends not only on the set of intervals but also on the properties of the structures, which are conditioned by the requirements imposed on the correspondence between the intervals and their supports (pairs of primary elements).8 However, a set of intervals and the properties of structures are not the only objects that determine a set of systems present, or rather thought of within the SPO. 7 By referring to the objects described here as “structures,” we use the term essentially in the same

sense as it is used in mathematics (so to speak, adhering to the mathematical tradition of word use [6]). 8 Such a requirement, for example, is that mutually inverse intervals correspond to mutually inverse pairs. Below these requirements are formalized as properties of the mapping ϕ, 3.1.

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There is a set of interval systems in the SPO, the existence of which logically precedes the existence of all the other SPO systems. Among all systems, possible at a set of intervals of the SPO, they have a special status: they determine the presence of systems within the SPO. To put it a little more rigorously, in the SPO there is a set of systems such that any system belonging to the SPO is either equal to one of them, or is a subsystem of one of them, or is a conjugation of some of these systems, or is a subsystem of the conjugation of some of these systems. Let us call systems of this set the primary systems of the SPO.9 From the familiarity with musical texts, from musical practice, finally, from the elementary theory of music, we know about the special objects that are present in the thinking of persons who create or perceive musical texts. These objects logically exist before the text, before the act of creating a pitch-meaningful, that is, a tone aggregate. Every act of creating a text in the aspect of the formation of a pitch structure is a combination, conjugation of these objects or their fragments, or conjugation of their sub-objects within their limits. These objects, that is, primary systems, are known to us mainly as chords and scales (they may include systems corresponding to unit intervals). For example, the combination of chord structures creates a cumulative structure and the system of this structure is thought of within the SPO not as an independent object, but as a conjugation of systems corresponding to the combined chords and “intrachord” intervals. Even more obvious is the example of constructing a melodic line within a certain scale: the structure of such a melody can have a system that is not the scale in its entirety, but is its subsystem. Or a phenomenon known as “addition to a chord of a non-chord tone”, which is the formation of a structure whose interval system is thought of as a conjugation of a system corresponding to a chord, and systems corresponding to intervals determined for pairs, each containing a nonchord element and one of the chord elements. (Of course, these examples are among the simplest and the most obvious). Approaching primary systems from the set theory positions, we must recognize, and recognize rightly, that primary systems form a subset in the set of all systems possible at the set of SPO intervals. However, in the structural-pitch thinking they have a special logical status: no interval system can exist in the SPO outside of one of the above relations to the primary systems. Balancing somewhere on the verge of analogy or even metonymy, we could say that primary systems are similar to hyper-intervals of the SPO: if intervals determine on the set of primary elements binary relationships of tone determination, then primary systems determine similar relationships of higher “arities”. 2.5 Conjugacies of Interval Systems. Primary Conjugacies. The Aggregate of All SPO Systems Conjugations of interval systems are interval systems and, as such, are determined by the set of SPO intervals and properties of structures. Moreover, conjugations are also 9 In the SPO there may be primary systems corresponding to unit intervals. However, the system’s

correspondence to the interval does not imply the identity of one and the other. It begs to assume that a unit interval is the simplest system, however, this is not true if even because interval is an object determining the tone on the pair of primary elements and the interval system is a structure equivalence class, see 3.1 Note 1.

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determined by the special class objects necessarily present in the SPO, which we call conjugacies. Conjugacy of systems is a situation in which there is a conjugation. Each conjugacy is characterized by certain systems and the way they are conjugated.10 To any conjugacy of systems there corresponds their conjugation (so to speak, the resultant for this conjugacy). For a certain set of systems, there may exist several conjugacies and their corresponding conjugations; a certain system may correspond to several conjugacies. For all the systems possible for a set of SPO intervals, a set of conjugacies is determined. However, according to the stated on the primary systems, in the SPO are thought of only such conjugacies which involve only primary systems or their subsystems. And, along with the set of primary systems, there is another determining object in the SPO – a set of primary conjugacies, which is singled out from the set of all possible conjugacies of primary systems. Thus, the systems thought of within the SPO in the first approximation are defined as subsystems of systems corresponding to primary conjugacies. (In the formal section, 3.4, an exact definition of the conjugacies and systems thought in the SPO, is provided). In musical practice, the primary conjugacies relate to such objects as the rules of chord connection, the rules of building melodic lines (melodic conjugations of intervals), the figures of voice leading. (We should note that the term “rules” is used by us in the functional meaning, not in the meaning of prescriptions, generally accepted or codified conventions. The rules here are the mental requirements in accordance with which pitch structures are forming, and these requirements are presented in objects such as primary systems and primary conjugacies.) 2.6 Some Comments We note that there is a minimal requirement to the graph of interval structure, which provides the integrity of the structure in the general case. This is the requirement to have a central vertex. A requirement of a strongly connected graph [5, p. 63] would be stronger: it provides an indirect determination of the tone for each primary element relative to each other. By the strongest requirement, the graph relation includes all ordered pairs of primary elements (i.e. there is an “arrow” from each vertex to each other). Structures with such graphs and the systems represented by them we will call complete. (Below we will demonstrate that the graph of any interval structure has loops at each vertex, 3.1). It is a familiar notion that if there is a pair of adjacent intervals, then there must also be a third, so to say, an aggregating interval. Also common is the notion that for every interval there is an inverse one. These notions are associated with the influence of instrumental culture; in addition, they are influenced by the mathematical comprehension of music, in particular the inertia of the Pythagorean tradition.11 In the general case, they are not true. 10 Further (in the formal section of the study, 3.3) the conjugacies are considered in detail and in

general. Here we explain: the conjugacy of some set of systems takes place if there is a set of representatives of these systems such that the graphs of some pairs of representatives intersect in such a way that a common graph with a central vertex is formed. 11 Since ancient times, “musical sounds” are identified with numbers from such a set, in which for every element there exists an inverse one, for a pair of relations a to b, b to c there is a relation a

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Also, in pitch thinking it is not necessary to have an encompassing system, that is, such, in which any system, possible at a set of intervals of the SPO, is a subsystem. An encompassing system is a characteristic of only some logically possible forms of SPO (this thesis is logically obvious; however, the evidence of this is numerous in early music, vividly represented in Medieval and Renaissance one, for example, in the accidental chromatics of Willaert type; in general, they can be found in music of any era, see Adrian Willaert, Pater Noster, mm. 10, 11, 36–38, 106–111 [17, pp. 11–14, see also 13]).

3 Formal Definitions 3.1 Key Concepts  is a set. This set is taken as a basic object, without determining its properties. We set P ⊂  × , with ∀a   (a, a)  P.  is a universal support of the SPO, its elements are called the primary elements of the SPO. I is a set with the following properties: • • • • •

there is a distinguished element there is a subset Inv ⊂ I of inversible elements, ∀α  Inv ∃! α−1  I (α−1 )−1 = α

Elements of the set I are called intervals. The subset Inv can consist of a single distinguished element, can contain some elements of I, or ultimately, this subset may equal I. We set the mapping ϕ: P → I with the following properties: If (a, b)  P and (b, a)  P, then ϕ(a, b) = ϕ(b, a)−1 If (a, b), (b, c), (a, c), (e, f), (f, g), (e, g)  P and ϕ(a, b) = ϕ(e, f), ϕ(b, c) = ϕ(f, g), then ϕ(a, c) = ϕ(e, g) (Instead of ϕ((a, b)) here and onwards we write ϕ(a, b).) The set of intervals is introduced initially as a set of abstract objects that have some properties. Through the mapping ϕ, intervals are defined as equivalency classes on the set P. We will call P the set of interval supports. For k 1, we determine Sk () = {s ⊂  | #s = k}. We single out from Sk () a set of such k-element subsets of , within which P forms a directed graph with at least one to c. And the properties of these numbers are transferred to pitch-thinking objects [16, see also 12].

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central vertex. We should elaborate: for X  Sk () we can determine GX = {(a, b)  P | a, b  X}. Then Nk = {X  Sk | GX forms a graph with a central vertex on X}. Elements of the set Nk will be called supports of interval systems of order k. νk is a set. We set the mapping γk : Nk → νk with the following property: if for X, Y  Nk there exists a bijection λ : X → Y such that ∀a, b  X. (a, b)  P ⇔(λ(a), λ(b))  P and ϕ(a, b) = ϕ(λ(a), λ(b)). then γk (X) = γk (Y). νk is introduced as an abstract set. Elements of νk are interpreted as interval systems of order k. Interval systems of order k are defined through the mapping γk as equivalence classes on Nk , i.e. on the set of their supports. The supports of interval systems were previously named representatives of interval systems. Note 1. P and N2 are different objects. X  P is an ordered pair of elements of . Y  N2 is a two-element subset of  such that in Y × Y there are either three or four pairs from P. That is, for Y = {a, b}  N2 GY = {(a, a), (b, b), (a, b)}, or GY = {(a, a), (b, b), (b, a)}, or GY = {(a, a), (b, b), (a, b), (b, a)}. For Y  N2 γ(Y) is an interval system corresponding to the interval α = ϕ(a, b): (a, b)  Y × Y and (a, b)  P. Note 2. The scheme of interval system α  νk is defined as following: is a directed graph. such that (a, b) ξ: G → I for which there is a bijection  G ⇔ (π(a), π(b))  P and ξ(a, b) = ϕ(π(a), π(b)). where X is any α support, i.e. γk (X) = α (it does not matter which exactly support we choose). 3.2 Some Generalizations and Definitions  νk N = Nk ν= k≥1

k≥1 γ : N→v

γ =



γk

k≥1

ν is a set of all interval systems, which is determined by the mapping ϕ for a given I. N is a set of all interval system supports. For X  N, a pair (X, γ (X)) is called interval structure. For the interval system α  ν any X  N such that γ(X) = α is called a support of this interval system. An interval system can have many supports. For interval systems α, β  ν α is called a subsystem of β if ∃A, B  N: γ(A) = α and γ(B) = β and A ⊂ B. ∀a   ∀K ⊂  ∃τK (a) = {(b, ϕ(a, b)) | b  K and (a, b)  P} For (a, K): a  K and K  N τK (a) is called a tone. Tones are determined in interval structures. Elements of  are interpreted as tone supports. Note 3. For a   K ⊂  we can define the pitch value of a in relation to K as a set τK (a). This set can be empty. However, if a  K, τK (a) is not empty, as in this case . T inv., for any element of  (a, ϕ(a, a))  τK (a). Let K = {a}, then

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a tone is determined relative to the set consisting of this element, and it is determined by the distinguished element of the set I. The distinguished element of the set I can be conditionally called zero interval. 3.3 Conjugations and Conjugacies of Interval Systems Let the interval systems α, β  ν and ∃A, B  N: γ(A) = α and γ(B) = β and and A ∪ B  N. Then, for α, β an interval system γ(A ∪ B) is determined, which is called a conjugation of α and β. The very situation in which a conjugation takes place is called conjugacy. α and β can have several conjugations or can have none. Moreover, for the supports A and B the intersection can belong to N or can not belong to N. In the first case, an interval system γ(A ∩ B) is additionally determined, which can be called a linking system for α, β. Let the arbitrary aggregate C ⊂ ν be given. And let the given set of supports D ⊂ N have the following properties: • ∀α  C ∃A  D: γ(A) = α • ∀A  D γ(A)  C . If (D, G) is a connected For D we determine graph, then D is called a conjugacy support for C. Meanwhile,    A γ A∈D

is called the conjugation of the aggregate C, and the aggregate C is called a cluster. For the cluster C, we determine a set of all conjugacy supports . C is a set, its elements are interpreted as conjugacies of the cluster C. We set the mapping.

and it has the following property: if E, and there exists a bijection   η: A→ B A∈E

B∈F

such that the mapping η* : E → F η* (X) = {η(x) | x  X}. • is set (image of every X  E in F) • is a bijection • ∀X  E γ(X) = γ(η* (X)) then ψ(E) = ψ(F).

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We should note that in this case it will be true that       γ A =γ B A∈E

B∈F

that is, equal conjugacies have equal conjugations. Therefore, for the conjugacy α  C we can determine ασ  ν, which is a conjugation for α. C is introduced as an abstract set. Through the mapping ψ the conjugacies of the cluster C are defined as equivalence classes on the set of all supports of conjugacies of the cluster C (in the same manner, intervals and interval systems were previously defined).  C

= C

where the union is done for all clusters determined by the mapping ϕ for a given I. That is, is a set of all the conjugacies set by the mapping ϕ for a given set of intervals of the SPO. if there are supports S, R (for σ and ρ respectively), as well as an For σ, ρ 

injection   ι: X→ Y X∈S

Y∈R

such that the induced mapping ι*: S → R is also an injection. We should note that the set consisting of a single interval system is considered as a cluster. , Note 4. The scheme of the conjugacy σ is a triplet ( , U, λ), where is a set, , λ: U → ν having the following properties: meaning •

• the graph {(X, Y) | X, Y ∈ U and X ∩ Y = ∅} is connected on U, for which there exists a bijection

such that η* : U → E is also a bijection, and ∀X  U λ(X) = γ(η* (X)), where E is a support of conjugacy σ. From the properties of the mapping ψ it follows that it is not important which conjugacy support E we choose.

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3.4 Final Definitions: Interval Systems and Conjugacies of Interval Systems of the SPO μ ⊂ ν Elements of μ are interpreted as primary interval systems. We distinguish a set of all clusters, which involve only interval systems of μ. there exists at least one conjugacy support for C}

is a set of all conjugacies supports for all clusters of . μ is a set of all conjugacies involving interval systems of μ. M ⊂ μ . Elements of the set M are interpreted as objects that determine which conjugacies of the primary systems are thought of within the SPO. Elements of M are called primary conjugacies of SPO.  is a set of all the conjugacies of the SPO. σ = {α σ |α ∈ } σ is a set of all the interval systems of the SPO.

4 Final Notes The content of extratextual SPO is a fragment of own content of SPO as a whole. The stated further applies only to the extratextual SPO. “Extratextual” before “SPO” will further be omitted. The sequence of definitions provided in the paragraph 3 is a formal definition of the SPO. The definition of the content of the SPO is also derived from this sequence. In other words, using this sequence, it is possible to formally present the internal musical content in one of its aspects, structural-pitch one. The form of content of the SPO is a form of content of structural-pitch thinking in general; the content of some SPO is the content of structural-pitch thinking individualized in one way or another (in particular, personalized and taken in some its state). The SPO content is presented as a triplet (I, μ, M), where I is a set of intervals, μ is a set of primary systems, M is a set of primary conjugacies. I is the elementary condition of the SPO, μ is the primary condition of the SPO, and M is its condition of the highest order. Let O be some SPO. Then its content is a triplet of sets (IO , μO , MO ), that is, a collection of specific objects that form these three sets. The triplet (IO , μO , MO ) together with the SPO relations determines all systems (and, accordingly, structures) of O, pitch structures of texts, in which O is the organizing factor of the structural-pitch aspect. By varying the conditions of the SPO, i.e. by determining the elementary content of the sets IO , μO , MO , and setting additional requirements to the objects of these sets12 , we can build a typological series of SPO. Here are examples of additional requirements: 12 We should note that the requirements for objects from these sets can be formulated as

requirements for objects derived from them.

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• ∀α  IO ∃α−1  IO meaning IO = InvO (for any interval there exists an inverse one) • ∀α  IO ∃Y  N2 : γ(Y)  μO and ∃(a, b)  Y × Y: ϕ(a, b) = α (for each interval there exists a corresponding primary system) • ∃ε  IO which is a special interval having the property: ∀α  IO ∃K ⊂ , elements of which can be ordered: K = {k1 , k2 , …, kn }, meanwhile ϕ(k1 , kn ) = α and ϕ(k1 , k2 ) = ϕ(k2 , k3 ) = … = ϕ(kn-1 , kn ) = ε (there is a forming interval, like a semitone in chromatic) • the presence of an identity similar to an octave one • completeness of primary systems (μO elements) of a certain class, or all primary systems • completeness of all SPO systems • ∃ρ  μO : ∀δ  σ O δ is a subsystem of ρ (there is an encompassing system), etc. In the series constructed in this manner, naturally, there are such SPO that we do not meet in musical practice or indicate phenomena that may arise. But other SPO of this series characterize the pitch thinking of individuals at some time periods, as well as the collective pitch thinking in different cultures and epochs.

References 1. Bershadskaya, T.S.: Harmony as an element of a musical system. [Gapmoni kak lement myzykalno cictemy]. Part I. Problems of theory, Ut, St. Petersburg, pp. 7–112 (1997) 2. Bershadskaya, T.S.: Lectures in Harmony. [Lekcii po gapmonii]. Muzika, Leningrad (1978) 3. Bershadskaya, T.S.: The music of noises: is it music? [Myzyka xymov – myzyka li? (Pazmyxleni o ctatyce ickycctva zvykov).]. In.: Bershadskaya, T.S. (ed.) Articles From Various Years. [Ctati paznyx let], vol. 2, pp. 125–128. Kompozitor, St. Petersburg (2019) 4. Bershadskaya, T.S.: On some analogies in the structures of verbal language and musical language. [O nekotopyx analogix v ctpyktypax zyka vepbalnogo i zyka myzykalnogo]. In.: Bershadskaya, T.S. (ed.) Articles From Various Years [Ctati paznyx let], pp. 234–294. Soyuz Khudozhnikov, St. Petersburg (2004) 5. Bondy, A., Murty, U.S.R.: Graph Theory. Graduate Texts in Mathematics. Springer, London (2008) 6. Bourbaki, N.: L’Architecture des mathématiques. In: Le Lionnais, F. (ed.) Les grands courants de la pensée mathématique, p. 35–47. Cahiers du Sud (1948) 7. Dahlhaus, C.: Die Idee der absoluten Musik. Bärenreiter-Verlag, Kassel, Basel, Tours, London, und Deutscher Taschenbuch-Verlag, München (1978) 8. Dufourt, H.: Timbre et espace. Le timbre: Métaphore pour la composition. Textes réunis et présentés par J.-B. Barrière, pp. 272−281. I.R.C.A.M. et Christian Bourgois Éditeur, Paris (1991) 9. Fétis, F.-J.: Traité complet de la théorie et de la pratique de l’harmonie. Neuvième édition. G. Brandus et S. Dufour, Paris (1867) 10. Garbuzov, N.A.: Zone Nature of Pitched Hearing. [Zonna ppipoda zvykovycotnogo clyxa]. Edition of the Academy of Science of the USSR, Moscow-Leningrad (1948) 11. Hanslick, E.: Vom Musikalisch-Schönen. Ein Beitrag zur Revision der Ästhetik der Tonkunst. R. Weigel (1854)

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12. Klein, F.: Elementarmathematik vom Höheren Standpunkte Aus: Arithmetik · Algebra · Analysis. Die Grundlehren der Mathematischen Wissenschaften 19/1, pp. 31–40. Springer, Heidelberg (1924) 13. Kroyer, Th.: Die Anfänge der Chromatik im italienischen Madrigal des XVI. Jahrhunderts. Breitkopf & Härtel, Leipzig (1902) 14. Schuijer, M.: Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts. Eastman Studies in Music. University of Rochester Press (2008) 15. Solomos, M.: From Music to Sound: The Emergence of Sound in 20th- and 21st-Century Music, 1st edn. Routledge, Milton Park (2019) 16. van der Waerden, B.L.: Die Harmonielehre der Pythagoreer. In: Hermes. Band 78, Heft 2, pp. 163–199 (1943) 17. Willaert, A., Zenck, H. (ed.): Motetta IV vocum, Liber secundus. Adriani Willaert opera omnia, vol. 2. Corpus mensurabilis musicae. American Institute of Musicology, Rome (1950)

What Are Musical Intervals? A Question Recharged via an Algebraic Theory of Measurement Celina Richter and Stefan E. Schmidt(B) Technische Universität Dresden, 01062 Dresden, Germany [email protected] http://wwwpub.zih.tu-dresden.de/~schmidt2/

Abstract. Everybody knows what musical intervals are, right?! Not so fast. In physics, folks tend to think of frequencies and proportions, while in ancient Greece, they had a monochord to get a grip on intervals. In psychoacoustics, people prefer the concept of difference of pitch, or just say that intervals can be added. In music cognition, we learn that tonal music on the white keys of the piano doesn’t care so much about sound and frequencies but more about the number of steps from one tone to another. Bobby McFerrin demonstrates with an audience how that works for pentatonic music. However, there is an algebraic theory of measurement which gets this all and much more under one umbrella. Keywords: Musical intervals · Algebraic measurement

1 Motivation A most fundamental concept in music is that of a musical interval, which essentially refers to a pair of tones. Musical intervals are interpreted either as sequential events or as simultaneous events. In this context, we want to consider them as elementary units of thought. For example, a person who wants to realize intervals on the monochord, has to play them sequentially even if he wants to think them simultaneously. An extended unit of thought is given by a path of musical intervals; it arises from two or more consecutive tones. And again, we raise a question: Is a path of musical intervals more like a melody or rather an arpeggio of a chord? So far, we have not distinguished whether these tones are, let’s say, pairs of keys of the piano, or maybe, written notes or played notes. Pairs of keys of the piano (without sound) and pairs of written notes will be considered as so-called syntactic musical intervals, while pairs of played notes will be referred to as semantic musical intervals. To model this systematically, we introduce the notion of an abstract measurement setup. In our contribution, we claim to be novel, though there is a lot of related literature. But our approach differs from others in the following way: We are able to look into partial systems of musical intervals. For example, if we tune a piano in the Pythagorean © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. D. Khannanov and R. Ruditsa (Eds.): WWMC 2021, CRSM 9, pp. 18–26, 2021. https://doi.org/10.1007/978-3-030-85886-5_2

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temperament (via just intonation based on the pure fifth) then, after eleven steps, we have a gap - and we simply stop; otherwise, we would go on and on, and would need infinitely many keys (even within an octave). Within this framework, we ask: Which musical intervals (derived by paths of pure fifths) are feasible? In particular, if we tune a cello in pure fifths, then the formal interval Cd (resulting from the path (CG, Gd)) will be feasible but Ca (resulting from (CG, Gd, da)) maybe not [1–4].

2 A Refined Approach to an Algebraic Theory of Measurement – Tailored to Capture a General Theory of Musical Intervals Our first goal is to lay out the algebraic foundations of our considerations. Here a most elementary structure we want to work with, is that of a monoid. Definition 1. A triple M = (M , ∗, ε) is named monoid. if M is a set with a binary operation ∗: M × M → M , (x, y) → x ∗ y and a fixed element ε ∈ M such that: ∀x, y, z ∈ M : (x ∗ y) ∗ z = x ∗ (y ∗ z) ∀x ∈ M : ε ∗ x = x = x ∗ ε The monoid is called commutative, if additionally it holds: ∀x, y ∈ M : x ∗ y = y ∗ x. The monoid M forms a group, if every of its elements is invertible, that is: ∀x ∈ M ∃y ∈ M : x ∗ y = ε = y ∗ x. To understand this definition better, we want to have a look at the most natural example. Example 1. Let N := {0, 1, 2, ...} be the natural numbers, then Nadd = (N, +, 0) is named the additive monoid of the natural numbers. This monoid is commutative. Example 2. Let Z := {..., −2, −1, 0, 1, 2, ...} be the set of integers, then Zadd := (Z, +, 0) forms a commutative group. Example 3. Let A be a set called alphabet and let ε be an element not contained in A. Then let Word(A): = Word(A, ε) denote the set of all words over A, that is: Word (A) := {w|∃n ∈ N+ ∃a1 , . . . , an ∈ A : w = (a1 , . . . , an ) } ∪ {ε}. Here ε will be called the empty word. Further let ⊗ be the binary operation on Word(A), called concatenation of words, given by: v ⊗ w := (c1 , ..., cm , a1 , ..., an )

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for all non-empty words v = (c1 , . . . , cm ) and w = (a1 , . . . , an ) over A, and let ε ⊗ w := w =: w ⊗ ε for all words w ∈ Word(A). Then Word (A) := (Word (A), ⊗, ε) is a monoid, called the word monoid over A.   Definition 2. For monoids M = (M , ∗, ε) and M = M , ∗ , ε , a map ϕ: M → M

forms a morphism from M to M , if the following hold:

∀x, y ∈ M : ϕ(x ∗ y) = ϕ(x) ∗ ϕ(y) ϕ(ε) = ε

If additionally, ϕ is bijective, ϕ forms an isomorphism from M to M . Example 4. Let A = {a} be the 1-element alphabet consisting of the letter a. Then the map ϕ : Word (A) → N, which maps for every n ∈ N+ , the word w = (a, . . . , a) ∈ An to n and the empty word to 0, forms an isomorphism from Word (A) to Nadd . N+ := {1, 2, 3, ...} denotes the set of positive integers. Now we want to extend the defined monoid to an abstract path domain, so we add two sets to the structure of the monoid. Definition 3. An abstract path domain is a triple T := (A, T , M) consisting of a monoid M = (M , ⊗, ε) and subsets A ⊆ T ⊆ M, so that the following holds: • ∀x ∈ M \{ε}∃n ∈ N+ ∃a1 , . . . , an ∈ A : x = a1 ⊗ . . . ⊗ an That is, A generates M. • For := {(s, t) ∈ M × M |∃x, y ∈ M : x ∗ s ∗ y = t } the following holds: ∀s, t ∈ M : ε = s t ∈ T ⇒ s ∈ T . We can interpret the set A as a set of arrows and T as a set of paths in T , and M is the structure monoid of T . Then s t means, s is a subpath of t. So, the second bullet point states, that T is closed under nontrivial subpaths. A second time we want to extend this structure. This time we add a map Prod, a set V , and another map ρ [11,17]. Definition 4. An abstract action domain is a quadruple T := (T , Prod , V , ρ) ∩ ◦: consisting of an abstract path domain T = (A, T , M), where M = (M , ⊗, ε) is a monoid; a map Prod: T → A; a subset V of A; and a map ρ : T → V × V with the induced maps σ := π1 ◦ ρ and τ := π2 ◦ ρ satisfying the following properties: (A0) ∀a ∈ A : Prod (a) = a

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(A1.1) ∀u ∈ T ∀x, z ∈ M : x ⊗ u ⊗ z ∈ T ⇒ x ⊗ Prod (u) ⊗ z ∈ T (A1.2) ∀u, w ∈ T : u ⊗ w ∈ T ⇒ Prod (Prod (u) ⊗ Prod (w)) = Prod (u ⊗ w) (A2.1) ∀u ∈ T : ρ(Prod (u)) = ρ(u) (A2.2) ∀a ∈ V : ρ(a) = (a, a) (A2.3) ∀u, w ∈ T \{∈} : u ⊗ w ∈ T ⇒ τ (u) = σ (w) (A3.1) ∀u ∈ T ∀x ∈ M : x ⊗ u ∈ T ⇒ x ⊗ σ (u) ⊗ u ∈ T (A3.2) ∀u ∈ T ∀x ∈ M : u ⊗ x ∈ T ⇒ u ⊗ τ (u) ⊗ x ∈ T (A3.3) ∀u ∈ T : Prod (σ (u) ⊗ u) = Prod (u) = Prod (u ⊗ τ (u)) Finally, we come to the central algebraic concept of our paper.

  Definition 5. An abstract measurement setup is a triple M = T, M,  consist  ing of an abstract action domain T = T , prod , V , ρ with T = (E, T , W) and W = (W , ⊗, ε); a monoid M = (M, +,0); and a measurement map  = W → M, which is a monoid morphism satisfying:   ∀u ∈ T :  Prod (u) = (u) ∀p ∈ V : (p) = 0 Comment: Here, the abstract action domain is the domain of what we measure, the measurement monoid is wherein we measure, and the measurement map says how we measure. The next definition will enable us to construct for any abstract action domain its universal measurement monoid and its universal abstract measurement setup. Definition 6. Let M = (M , ∗, ε) be a monoid. a) A congruence relation on M is an equivalence relation θ on M , such that x 1 θ y1 and x 2 θ y2 implies x 1 ∗ x 2 θ y1 ∗ y2 for all x 1 , x 2 , y1 , y2 ∈ M. b) Let θ be a congruence relation on M. Then x θ: = {y ∈ M| x θ y} is the congruence class of x ∈ M, and M/θ: = {x θ|x ∈ M} denotes the set of all congruence classes of M over θ . It follows that M/θ := (M /θ, ∗θ , εθ ) with ∗θ : M/θ × M/θ → M/θ , (xθ , yθ ) → (x ∗ y) θ is a monoid, called the factor monoid of M over θ . c) The set intersection of congruence relations on M is again a congruence relation on M. For a set X ⊆ M × M let X M denote the intersection of all congruence relations on M which contain X. Indeed, with respect to set inclusion, X M is the least congruence relation on M which contains X. d) It is easy to verify that any monoid morphism ϕ on M gives rise to a congruence relation on M via its kernel, defined as:

ker(ϕ) := {(x, y) ∈ M × M |ϕ(x) = ϕ(y)}.   Construction. Let T = T , Prod , V , ρ be an abstract action domain with T = (E, T, W):

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1) Then the factor monoid MT : = W/θ  T with   θT := {(u, Prod (u))|u ∈ T } ∪ (p, )| p ∈ V W will be called the universal measurement monoid of T. We set (MT ,+T ,0T ) := MT . 2) For the map T : W → MT , x → x θT it follows, that MT : = (T,MT ,T ) is an abstract measurement setup, called the universal abstract measurement setup of T. Now we have finished all preparations and are able to come to the main results of this section. First we have to discuss the splitting theorem for monoid morphisms, so that we can use it to prove the universal property of a universal abstract measurement setup of an abstract action domain [7–9]. Theorem 1. Splitting theorem for monoid morphisms. Let ϕ 1 be a surjective monoid morphism from the monoid M = (M , ∗, ε) to M1 = (M1 , ∗1 , ε1 ) and let ϕ 2 be a monoid morphism from M to M2 = (M2 , ∗2 , ε2 ) with ker(ϕ 1 ) ⊆ ker(ϕ 2 ). Then there exists a unique monoid morphism ϕ from M1 to M2 with ϕ2 = ϕ ◦ ϕ1 . Proof

– uniqueness: Let ψ be a monoid morphism from M1 to M2 with ϕ2 = ψ ◦ ϕ1 . ⇒ for all x in M it holds that ϕ2 (x) = ψ(ϕ1 (x)) ⇒ ψ : ϕ1 (x) → ϕ2 (x) ⇒ ψ must be unique, since ϕ1 is surjective

– existence: Let ϕ: M 1 → M 2 , ϕ 1 (x) → ϕ 2 (x). We want to show, that ϕ is well-defined. Let t, x ∈ M with ϕ 1 (t) = ϕ 1 (x). Then (t, x) ∈ ker(ϕ 1 ) ⊆ ker(ϕ 2 ), which implies ϕ 2 (t) = ϕ 2 (x). Furthermore: ϕ(ϕ1 (x) ∗ 1 ϕ1 (y)) = ϕ(ϕ1 (x ∗ y)) = ϕ2 (x ∗ 1 y) = ϕ2 (x) ∗ 2 ϕ2 (y) = (ϕ(ϕ1 (x)) ∗ 2 ϕ(ϕ1 (y)) and ϕ(ε1 ) = ϕ(ϕ1 (ε)) = ϕ2 (ε) = ε2 Theorem 2. Universal property of a universal abstract measurement setup of an abstract action domain. Let T = (T , Prod , V , ρ) be an abstract action domain with T = (E, T , W), W = (W , ⊗, ε). Then for every abstract measurement setup M = (T,M,) there exists a unique monoid morphism ϕ: MT → M with  = ϕ ◦ T .

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Proof. From (Prod(u)) = (u) for allu ∈ T and (p) = 0 = (ε) for all p ∈ V , it follows by definition that θT ⊆ ker  holds. Since T : W → MT , x → x θT is a surjective monoid morphism with ker(T ) = θT , we conclude ker(T ) ⊆ ker  . Now Theorem 2 follows from the splitting theorem.

3 Musical Side An abstract action domain for syntactic musical intervals: Construction: Let P be a set of so-called points considered as formal tones (or tone names). If p and q are formal tones, then let the pair pq: = (p, q) denote the formal interval from p to q over P. In particular, for a formal tone p, its formal prime interval is given by pp. Let us now consider a set R of formal intervals over P, which contains all formal prime intervals over P. Then, a syntactic musical interval over P = (P, R) is defined as a formal interval over P, which is contained in R. Thus R denotes the set of all syntactic musical intervals over P. Important for us is the concept of path: A path of formal intervals over P is defined as a consecutive sequence of formal intervals over P, that is, a sequence of the form (p0 p1 , p1 p2 , . . . , pn−1 pn ), where p0 , . . . , pn are formal tones. A formal interval may be considered as path of length 1. The next step is to single out a set T, consisting of certain paths of syntactic musical intervals. In particular, we assume that T contains every syntactic musical interval and is closed under subpaths, that is, TI = (R, T, Word (R)) is an abstract path domain, called the abstract path domain over I: = (P, R, T ). Here, we refer to I as the input of TI . Interpretation: The input consists of the set P of formal tones, the set R of syntactic musical intervals (considered as ‘feasible’ intervals), and the set T of syntactic paths (considered as ‘feasible’ paths) of syntactic musical intervals. Next we want to extend TI to the abstract action domain over I. Let Prod I be the map from T to R which assigns to every path (p0 p1 , p1 p2 , . . . , pn−1 pn ) in T the interval p0 pn , that is: ProdI (p0 p1 , p1 p2 , . . . , pn−1 pn ) := p0 pn Since R contains for every formal tone p in P its formal prime interval p :=pp, every such interval is a syntactic musical interval. Let P := {p|p ∈ P} denote the set of all formal prime intervals over P. Finally, let ρ I be the map which assigns to every path (p0 p1 , p1 p2 , …, pn−1 pn ) in T the pair (p0 , pn ) of formal prime intervals, that is, ρ I (p0 p1 , p1 p2 , ..., pn−1 pn ) := (p0 , pn ). Then TI := (TI , ProdI , P, ρ I ) is an abstract action domain, called the abstract action domain over the input I = (P, R, T ). Remark 1. We consider TI as an algebraic formalisation of the concept of syntactic musical intervals in a certain musical situation, which depends on an input I = (P, R, T ).

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If M = (TI ,M,) is an abstract measurement setup over TI with measurement monoid M = (M, +, 0) and a measurement map  from Word(R) to M, then M contains semantic musical intervals, and  assigns to every syntactic musical interval its semantic musical interval - within the framework of the abstract action domain M. Remark 2. The existence of the universal abstract measurement setup of the abstract action domain TI leads to the concept of universal semantic musical intervals for every input I = (P, R, T )! [5, 14, 15].

Fig. 1. Tonnetz

The TONNETZ (see Fig. 1) can be viewed as abstract measurement setup of musical chromas based on the intervals fifth and major third. Arrows are interpreted as feasible syntactic musical intervals. If a path of syntactic musical intervals is considered as feasible, then so is every subpath. We can decide the feasibility of syntactic musical intervals. Our Theorem implies, there does exist the concept of ‘universal semantic intervals’. While syntactic intervals can be concatenated via Prod, semantic intervals can be added in a monoid. There are different degrees of ‘how semantic’ an interval is considered! [6, 10, 12, 13, 16].

Fig. 2. Feasible path example 1

    df , fa, ac , c e ∈ T ⇒ Prod df , fa, ac , c e = de ,   that is if df , fa, ac , c e is considered as a ‘feasible path’ of syntactic musical intervals, then the product Prod of this path is also considered as ‘feasible’. See Fig. 2.

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Fig. 3. Feasible path example 2

(Ac, ce, eg) ∈ T ⇒ Prod (Ac, ce, eg) = Ag Warning: (Ac, eg) ∈ / T. Prod(Ac, eg) is not defined. See Fig. 3 (Table 1). Table 1. Calculus of syntactic musical intervals Syntactic source Syntactic target σ (df ) = dd

τ (df ) = ff

xx for a tone x is a syntactical musical prime interval.

4 Summary Based on the algebraic concept of a monoid, we have developed a rather sophisticated general algebraic theory of measurement, which specifies to a general theory of musical intervals. In our current contribution, we have focused on the algebraic modeling of syntactic musical intervals - to single out feasible musical intervals within a framework of formal intervals. Our main mathematical result (Theorem 2) states, that every abstract action domain gives rise to a universal abstract measurement setup. Specified to musical intervals, this means, that for any given framework of syntactic musical intervals, there can be derived a universal concept of semantic musical intervals.

References 1. Agon, C., et al.: Mathematics and Computation in Music. Third International Conference, MCM 2011, Paris, France, June 15–17, 2011. Proceedings. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21590-2. http://slubdd.de/katalog?TN_libero_mab2)100 0254804 2. Klouche, T., Noll, T. (eds.): Mathematics and Computation in Music. First International Conference; MCM 2007, Berlin, Germany, May 18–20, 2007. Revised Selected Papers. Springer, Berlin (2009). ISBN 1865-0929. https://doi.org/10.1007/978-3-642-04579-0. http://slubdd. de/katalog?TN_libero_mab214556527 3. Cannas, S.S., et al.: Geometric Representation and Algebraic Formalization of Musical Structures; Représentations géométriques et formalisations algébriques de structures musicales, 27 November 2018. http://slubdd.de/katalog?TN_libero_mab2 4. Genuys, G., Allouche, J.-P., Andreatta, M.: Non-commutative homometric musical structures and chord distances in geometric pitch spaces; Etude de deux concepts mathématicomusicaux: l’homométrie non-commutative et les distances d’accords, 20 September 2017. http://slubdd.de/katalog?TN_libero_mab2

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5. Göller, S., Agon, C., Mazzola, G.: The Topos of Music Geometric Logic of Concepts, Theory, and Performance. Birkhäuser, Basel (2002). ISBN 3764357312. http://slubdd.de/katalog? TN_libero_mab23544898 6. Götze, H., Wille, R.: Musik und Mathematik. Salzburger Musikgespräch 1984 unter Vorsitz von Herbert von Karajan. Springer, Heidelberg (1985). https://doi.org/10.1007/978-3-64295474-0. http://slubdd.de/katalog?TN_libero_mab216397780 7. Harasim, D., Schmidt, S.E., Rohrmeier, M.: Axiomatic scale theory (2020). http://slubdd.de/ katalog?TN_libero_mab2 8. Harasim, D., Schmidt, S.E., Rohrmeier, M.: Bridging scale theory and geometrical approaches to harmony: the voice-leading duality between complementary chords (2016). http://slubdd. de/katalog?TN_libero_mab2 9. Jacoby, N., Tishby, N., Tymoczko, D.: An information theoretic approach to chord categorization and functional harmony (2015). http://slubdd.de/katalog?TN_libero_mab2 10. Mazzola, G., Muzzulini, D., Hofmann, G.R.: Geometrie der Töne Elemente der mathematischen Musiktheorie. Birkhäuser, Basel [u.a.] (1990). ISBN 3764323531. http://slubdd.de/kat alog?TN_libero_mab26354 11. Noll, T.: Musical intervals and special linear transformations (2007). http://slubdd.de/katalog? TN_libero_mab2 12. Agon, C., Amiot, E., Andreatta, M., Assayag, G., Bresson, J., Manderau, J. (eds.) Mathematics and Computation in Music. Third International Conference, MCM 2011, Paris, France, June 15–17, 2011; Proceedings. Springer, Berlin (2011). ISBN 0302-9743. https://doi.org/10.1007/ 978-3-642-21590-2. http://slubdd.de/katalog?TN_libero_mab2)1000251500 13. Schlemmer, T., Schmidt, S.: A formal concept analysis of harmonic forms and interval structures. Ann. Math. Artif. Intell. 59, 241–256 (2010). https://doi.org/10.1007/s10472-0109198-6 14. Tymnik, G. et al.: Temporäre Harmonisierung des monotonalen Tinnitus mittels transponierter Musik – Smetana-Phänomen, 19 January 2018. http://slubdd.de/katalog?TN_libero_mab2 15. Tymoczko, D.: A Geometry of Music Harmony and Counterpoint in the Extended Common Practice. Oxford University Press, New York [u.a.] (2011). ISBN 0195336674. http://slubdd. de/katalog?TN_libero_mab215459349 16. Tymoczko, D.: Geometry and the quest for theoretical generality (2013). http://slubdd.de/kat alog?TN_libero_mab2 17. Winkler, J.T.: Algebraische Modellierung von Tonsystemen Musiktheorie mit mathematischen Mitteln. Verl. Allgemeine Wissenschaft, Mühltal (2009). ISBN 9783935924078. http:// slubdd.de/katalog?TN_libero_mab214365333

Language and Narrative

Thinking/Feeling Musical Narrative Vincent Meelberg(B) Radboud University, Erasmusplein 1, Nijmegen, The Netherlands [email protected]

Abstract. This essay investigates the narrative potentiality of music from an experiential point of view. Since narrativity can be considered the act of creating an interplay of tension and resolution by exploiting suspense, curiosity, and surprise, and the expressivity of music is constituted by the interplay of tension and resolution that can be identified in the musical sounds, any music that can be considered expressive has a narrative potentiality as well. This narrative potentiality is experienced through the body. Listeners literally feel the interplay of tension and resolution in their bodies and are provoked to make sense of what they are experiencing, which may lead to a narrative understanding of the music. Therefore, the study of the narrative potential of music necessitates a focus on listening as an act in which the entire body is involved. Moreover, listening to and creating musical narratives can be considered as forms of sonic thinking. Listening to music as a narrative implies a focus on what music can do to the bodies and minds of listeners. It informs us about the affective capacity of music as well as about how our bodies act and react as a result of being exposed to music. Keywords: Narrativity · Narrativization · Materiality of sound · Expression · Affect · Sonic thinking

1 Introduction What does it mean to create a musical event? What do we do when we are performing or composing music? Ultimately, music is energy. It is energy from a physical point of view, as the sounds that the music consists of are vibrations of air molecules. Music, however, is also energy in a different sense. Music has the power to move people, both physically and mentally. Consequently, music is a force, a sonic cultural expression that has an impact on listeners, performers, and composers alike, and through this force music performers and composers are able to express themselves. One of the manners in which human beings express themselves is via narrative. Narrative enables human beings to communicate ideas, feelings, and fictions. The question whether music can be narrative is discussed in several studies, such as Meelberg (2006) and Almén (2017). Most of these studies, however, approach musical narrativity from an analytical and what Sternberg (2010) calls an objective point of view. In this essay I will investigates the musical narrativity from an experiential point of view. More specifically, I will explore musical narrative in terms of what it does, or can do, rather than what it is, or can be. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. D. Khannanov and R. Ruditsa (Eds.): WWMC 2021, CRSM 9, pp. 29–40, 2021. https://doi.org/10.1007/978-3-030-85886-5_3

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First, I will discuss how the notion of narrative can be conceptualized in order to emphasize its performative and expressive characteristics. Following Sternberg, I will assert that narrativity is the act of creating an interplay of tension and resolution by exploiting suspense, curiosity, and surprise. Next, I will shift my focus to the manners in which listeners make sense of the basic building blocks of music, i.e. sound, and investigate how the materiality of sound can contribute to the narrative potentiality of music. I will argue that listeners literally feel the interplay of tension and resolution in their bodies, which implies that musical narrativity is, at least in part, an embodied experience. Finally, I will explore the possibilities for considering listening to and creating musical narratives as forms of sonic thinking. Sonic thinking is a thinking with and by means of sound, and listening to musical sounds as a narrative implies a focus on what music can do to the bodies of listeners. It is a form of sonic thinking about the ways in which music can affect listeners. It informs us about the affective capacity of music as well as how our bodies act and react as a result of being exposed to music.

2 The Concept of Narrative Human beings are a storytelling species. Humans have always told stories in words, images, and sounds. And storytelling is not just the way we humans communicate ideas and fictions. It is a general mode we think in, as Yanna Popova asserts: Stories are everywhere in human lives and storytelling is indeed part of all human cultures. We think in narrative, remember in narrative and interact in narrative. People tell stories in words, in pictures and in movement, in musical forms, and through increasingly diverse multimodal means. (Popova 2014: 1) We human beings survive in this world by trying to make sense of what we see, hear, feel, smell, and taste. In order to arrive at some kind of understanding of the world in which we live, we focus on elements that proved to be essential to our survival, while ignoring other elements. We try to deduct from things we experience certain actions that we have to take, interpreting particular events as causes of other events that have happened or will happen. In short, we try to grasp our world by turning it into a unified whole. And one of the methods we apply to create such a unity is narrativization; the act of interpreting a sequence of events as a story. Narratives function as accounts with which human subjects can make the events they undergo discursive; in other words, to turn them into experiences: Narrative is an integral part of our everyday lives. Narratives underline our interactions with one another, our understanding of space and place, and our individual sense of identity. Additionally, narratives are crucial within our understanding of wider society. (Anderson and Rennie 2016: 223) Thus, broadly speaking, there are two functions of narrative, which are interrelated: on the one hand, narrative can be regarded as a means to make sense of the world, to structure our experiences and to integrate these into a comprehensible whole. On the other hand, narrative functions as an account with which we can make our experiences

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discursive. Stories are both cultural objects and the manner in which we talk about those objects. Moreover, narrative is the manner in which we have access to other people’s experiences; it is a way to distribute individual experiences and knowledge. Referring to Jean-François Lyotard, Isobel Anderson and Tullie Rennie observe that “[…] narrative knowledge deals with the complex intertwining of time, space, communication and language, and therefore is a vital part of understanding the world and society” (2016: 223–224). In short: stories are crucial in representing knowledge, experience, beliefs, desires, and fantasies. It is one of the most important means by which we communicate. Narrative is an instrument for distributing and elaborating the perspectives that can be adopted on a given set of events. Stories aid in enriching the whole of the past, present, and possible future events that constitutes the foundation of human knowledge. Moreover, through narrative we can view ourselves as coherent individuals that have a clear place within the culture we live in. Shaun Gallagher observes that: [n]arratives address the why question as well as the how question. Clearly, our retrospective evaluations of our actions take the form of narrative; so do our prospective deliberations. What are we going to do, and why are we doing it? [...] Narratives are social products. They emerge relatively early in development and in circumstances involving child’s play they lead to we-narratives. Narratives also assist in helping us understand others. (2017: 469–470) By producing and listening to narratives, we place ourselves within a social environment; through stories both our particular place can be articulated, and knowledge of this environment can be gained. Storytelling thus appears to be fundamental to human culture. Narrativization – interpreting ourselves and the world we live in as a narrative – is a basic human strategy for coming to terms with time, process, and change. It is a means in order to make sense of the world and ourselves, to structure our experiences and to integrate these into a comprehensible whole. Elsewhere (Meelberg 2006) I suggested that narrative can be understood as a representation of a temporal development: a representative sequence of logically and chronologically related events. This conception of narrative is consistent with the above elaboration of how narratives are created and used by human beings, and can be regarded what Meir Sternberg (2010) calls an objectivist conception of narrative, and is in line with other objectivist definitions of narrative, such as the one articulated by Paisley Livingston: Narrativity is constituted by (or increases with) the representation of (1) events (2) as temporally ordered, (3) as causally related, (4) as unified (for example, as involving the same substance or topic), and as (5) actions where (6) the agent(s) encounters and contends with nonroutine obstacles to the realization of his or her goals. (2009: 28; emphasis in original) In this definition, too, representation, temporality, logic, and causality are highlighted. This is why Sternberg calls these kinds of definitions objectivist, as they define narrative and narrativity “[…] by the represented object. The tags for this object widely

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vary among, say, ‘content,’ ‘meaning,’ ‘semantics,’ ‘signified,’ ‘subject matter,’ ‘what,’ ‘mimesis,’ ‘representation,’ ‘fabula level’ ‘the told,’ the field or focus of reference, and so forth” (2010: 519). For Sternberg, an objectivist conception of narrative is too limiting, as it excludes certain forms of expression that could be considered acts of storytelling as well, but do not comply with one or more of the characteristics listed in objectivist definitions of narrative. Instead, Sternberg proposes to define narrative in terms of what it does, rather than what it is, or should be. “[N]arrative/narrativity is what it does to the experiencer in the discoursing” (643). Storytelling is an act that has an impact on the person or people the story is told to. This person may also be the one who is in the process of narrativizing something, as narrativization can be considered the simultaneous act of creating a story and simultaneously telling it to oneself during the creation of this story. Ultimately, Sternberg formulates the following definitions of narrative and narrativity: narrativity is “[…] the play of suspense/curiosity/surprise between represented and communicative time (in whatever combination, whatever medium, whatever manifest or latent form). Along the same functional lines, I define narrative as a discourse where such play dominates” (642). Storytelling is an activity that consists of playing with expectations. Storytelling means creating an interplay of tension and resolution. It is this interplay, the play of suspense, curiosity, and surprise that distinguish narrative from “[…] everything else, because they exhaust the possibilities of communicating, or (re)constructing, action: of aligning (‘twinning’) its natural early-to-late development toward a humanly unknowable future with its openness to untimely, crooked disclosure” (Sternberg 2010: 641). Narrativity is a property characterized by what it does, i.e. creating an interplay of tension and resolution by exploiting suspense, curiosity, and surprise, and this property may feature in varying degrees among different objects, events, and other phenomena, as Sternberg points out: “So narrativity is what it uniquely does, or has us do, or becomes of what we do, in the twofold process thrice compounded by suspense/curiosity/surprise; and narrative makes the most (as description makes the least) of narrativity’s doings, sui generis.” (642). Moreover, this conceptualization of narrative and narrativity does not presuppose a particular medium such as language, as any object, event, or phenomenon in principle has the potentiality to play with suspense, curiosity, and surprise. After all, this play happens in what Sternberg calls the (re)constructive mind, and as a result, “[…] they can map themselves on any surface form, not even necessarily an objective one, still less objective-looking, to produce the co-definitional objective time-sequence” (645– 646). Anything that has the capacity to provoke or suggest an interplay of tension and resolution in the mind of a human subject has a narrative potentiality. Conceptualizing narrativity as an interplay of tension and resolution implies that causality, or rather the suggestion of causality, is very important in narrative understanding. Tension and resolution can only be sensed if some kind of expectation is elicited, an expectation that is either met or not. Interpreting a sequence of events as an interplay of tension and resolution means considering these events as causally related, regardless of whether this relation is a reality or a projection of an apprehending subject. Objects that can be interpreted as containing events that are somehow – metaphorically or otherwise – causally related are more prone to elicit sensations of tension and resolution.

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3 Sound as Narrative Material In order to explore the possibilities of the narrative potentiality of music it is useful to have a proper understanding of how listeners make sense of the basic building blocks of music, i.e. sound. After all, if music does have a narrative potential, this means that its constituent parts, the sounds, have the ability to evoke a sense of suspense, curiosity and surprise, an interplay of tension and resolution in listeners. This again implies that listeners are able to make sense of sound in a very specific manner: they are able to interpret sounds as a sequence of events in which causal relations can be identified. The question thus is how sound allows for such an interpretation. Christoph Cox’s conceptualization of the materiality of sound might be helpful in answering this question. He maintains that this materiality consists of “[…] its texture and temporal flow, its palpable effect on, and affection by the materials through and against which it is transmitted” (2011: 149). Paul Simpson adds that “[…] the sound itself is precisely sound’s materiality, its body, its timbre, and about the resonance these produce” (2009: 2559). Sound thus is vibration, which is a temporal phenomenon, and the manner in which these vibrations manifest themselves as resonances constitutes the materiality of sound. At the same time, these very resonances are responsible for the expressive qualities of sound. Sounds resonate in listeners’ bodies. They do so not only in their ears but also as something that is felt (Gershon 2013; Goodman 2010). Sounds can literally move the bodies of listeners. Not only because bodies resonate as a result of being exposed to sounds, but also because these resonances can induce autonomous bodily reactions at an unconscious level. Sounds can induce frisson, which David Huron describes as “[…] chills running up and down your spine” (2006: 34). Frisson is an example of a bodily reaction to hearing sound that happens at an unconscious level. Sounds thus seem to be able to literally move the listener’s body and generate chills up and down the listener’s spine. At the same time, these bodily reactions motivate listeners to reflect on the sensations they are experiencing, to notice them, think about them, and try to make sense of them. Elsewhere, (Meelberg 2009) I suggested to call the sounds that elicit such responses sonic strokes. A stroke can be a slap, but a caress as well. Therefore, a sonic stroke can be both a sound that has an impact on the listeners’ bodies because of its volume, as Huron (2006) explains. As soon as listeners perceive a sudden, loud sound, their bodies shiver. A shock is running through their bodies, a shock that can literally be felt but cannot be controlled by the listeners who inhabit these bodies. Also, a sound can be a sonic stroke because it sounds very softly, or because it has a particular timbre or rhythm that, in some way, arouses listeners, for instance because it is surprising in a particular manner. In short: sonic strokes are acoustic phenomena that have an impact on the bodies of listeners. Consequently, music affects these bodies through sonic strokes. The materiality of sound, considered as resonances that can be felt, thus has affective qualities that, in turn, are responsible for the expressive qualities of sound, that is, the capacity of sound to instigate a change in listeners and to grasp their attention. Sound has this ability not because it represents or signifies something other than itself, but because of what it does, how it operates and what changes it effectuates (Cox 2011: 157).

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Walter Gershon suggests that the relation between affect and sound is even stronger. Not only is sound able to induce affects in listeners, affect itself appears to behave much like sounds do: [A]ffect seems to move like sound: ephemeral, liminal, haptic, lingering, deeply moving waves that operate within and outside perception. Although this is not necessarily surprising as the sonic is one mode in and through which affect operates, in light of continuing conversations about affect and how language falls short in its explanation, such comparisons may yet be theoretically and practically helpful. (Gershon 2018: 8) Affect moves like sound, and at the same time sound itself has affective qualities because it consists of sonic strokes. A sonic stroke is an impetus to thinking and reflection. It motivates listeners to reflect on the acoustic phenomena they are confronted with. It is an incitement to reflect on the sonic vibrations and to make sense of them. In this way the materiality of sound establishes relations between sonic phenomena and their interpretation by listeners. As Gershon puts it: “In sum, where resonances are alignments between the vibrational affects of at least two things, be they ideas, sounds, or feelings, what one is in fact resonating with are reverberations, the mediated, messy, information that are resonances in motion.” (2018: 6) Sounds are resonances, resonances that may lead to impressions, ideas, or feelings through sonic affection, while these ideas, impressions, and feelings themselves resonate in the perceiving subject as well. This is why Gershon asserts that the materiality of sound ultimately is political: “Whether conceptualized as something physical (something causing another thing to vibrate) or, especially, theoretical (an idea that causes waves of vibrational affect), reverberations and resonances are therefore also always political, the result of particular intentions and expressions.” (2) Sound and the manners in which its resonances have the potentiality to affect, and thus influence, listeners have ethical and political connotations. In sum, the materiality of sound enables the establishing of relations between sounds, listeners, and ideas. As a result, the resonances caused by sounds, i.e. their vibrational affect, incite listeners to make sense of the sounds. And it is this very same ability that is the reason why sound, and by extension music, has a narrative potentiality. Jarmila Mildorf and Till Kinzel point out that: [t]he very nature of sound makes it potentially narrative since sound moves and is received in time. If there is in addition a change in sound or sound quality we can already speak of a minimal narrative sequence because not only do we perceive a passing of time but also different sound events on that time axis. The criterion of eventfulness, which for many narratologists is a key criterion for defining narrative, can arguably be created through sound alone. (2016: 13) Sound is a temporal phenomenon, and the changes over time that can be perceived by listeners already constitute the suggestion of narrative. Listeners can establish relations between these changes, make sense of them and have expectations regarding further changes that may or may not happen. So, a sound that gradually increases in volume and after a certain point becomes quieter until the sound has stopped in itself has a narrative

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potentiality, Mildorf and Kinzel seem to suggest. And indeed, a case could be made that such a sound is able to instigate a play of suspense, curiosity and surprise, an interplay of tension and resolution. A sound that rises or lowers in volume may in fact be able to suggest suspense and create expectations in listeners, expectations that are either met or not. And all this is elicited by the resonances caused by sounds, their vibrational affect. Gershon even considers narratives themselves “[…] as forms of resonances and reverberations. Whether as the voice in your head as you read or outside of your body, voiced by or to others aloud, for example, stories are articulations of ideas, ideals, and possibilities” (2018: 3). Narratives are resonances because the ideas they articulate resonate within those to whom these narratives are told. Moreover, narratives often are structured as resonances and reverberations, Gershon suggests: Many if not most ideas and ideals are expressed as some form of narrative. And stories, in many ways follow the patterns and possibilities of reverberations that start as resonance that, in across layers of scale. For this reason, discussions of reverberations are in many ways also articulations about narratives. (3) Resonance and narrative thus appear to be intimately related. This, in turn, implies that the materiality of sound – the manner in which sonic vibrations manifest themselves as resonances that can be felt – is closely related to narrative as well. One of the reasons why such sounds may evoke such feelings of tension and resolution is because listeners literally feel these sensations in their bodies while listening. The body is not only literally touched by sounds, because the sound waves touch the eardrum and make it move, but also included because the body kinesthetically senses the interplay of tension and resolution produced by the sounds. It feels this interplay by sensing its dynamic and temporal flow. These kinesthetic sensations are the result of mirror neurons that fire when a subject performs a movement or observes a movement in another subject: similar neural activity is found in human beings when they perform an action as well as when they imagine or think about doing that same action (Kaag 2014). Performing actions and observing actions activate the same brain areas. Watching movement thus can lead to sensing this movement within the subject’s own body, as if the subject is actually performing this movement. This is also the case when it concerns the perception of sound. The body kinesthetically senses, and subsequently processes, the dynamics, the physical properties, of sound. Put differently: the materiality of sound, the manner in which sonic vibrations manifest themselves as resonances that can be felt, is kinesthetically sensed by listeners. As a result, the narrative potential of sound is the result of the interplay of tension and resolution is not only perceived aurally, but also physically felt. And it is the physical perception of the interplay of tension and resolution, in particular, that is responsible for the narrative potential of sound. As Richard Menary explains, human subjects tend to turn embodied, physical experiences into a narrative: “Narratives arise directly from the lived experience of the embodied subject and these narratives can be embellished and reflected upon if we need to find a meaningful form or structure in that sequence of experiences.” (2008: 76). And Menary is not the only one who stresses the crucial role the body plays in narrative understanding. Hydén (2013) points out that listening to a story is not only a

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bodily experience, but also relies on and makes use of previous bodily experiences that are made relevant through the active interpretation of story. It is because we have a body that we are able to make sense of narratives. Daniel Punday adds that “[t]he body [is] very much a matter of the ‘what’ of narrative rather than of its ‘how’” (2003: 6). Bodies are not only the content of narrative, but also part of its very fabric. There cannot be narrative without embodiment. Therefore, Punday asserts, narrative is corporeal: Narrative is corporeal not simply because it needs to use character bodies as a natural part of the stories that it tells, but also because the very ways in which we think about narrative reflect the paradoxes of the body – its ability to give rise to and resist pattern, its position in the world and outside of it, and so on. Narrative, then, always first and foremost depends upon a corporeal hermeneutics – a theory of how the text can be meaningfully articulated through the body even if narratology has frequently treated it, or seemed to treat it, as something quite different. (15) Narrative is understood through the body, or via a corporeal hermeneutics as Punday calls it. Understanding a narrative is not merely a cognitive activity, but one that incorporates the entire body, just as listening to and making sense of sound is an embodied act. Furthermore, as Hydén (2013) points out, stories are not based on representations of past experience. Instead, stories are entangled in experience, and experience is entangled in stories. Listening to and telling stories are embodied experiences, while embodied experience is the very stuff that stories are made of. Consequently, when studying narrative and narrativity, it is not sufficient to focus on texts and mental processes exclusively and ignore the body. Even though it could be argued that the construction of narratives ultimately happens in the minds of the perceivers of a story, the process through which these narratives are constructed is everything but disembodied. As Hydén puts it: “[T]he body in narrative research often is just the represented body – not the physical bodies that are actually present in the storytelling event; those bodies are often left out of the narrative analysis. Not including the actual bodies in the analysis becomes problematic in relation to certain groups of storytellers, and also has some theoretical implications.” (2013: 126). This also holds for musical narratives. As I explained above, the play of suspense, curiosity and surprise, an interplay of tension and resolution, which make up the narrative potentiality of music, is experienced in the body itself as a result of the materiality of sound. Listeners literally feel this interplay in their bodies and are provoked to make sense of what they are experiencing, which ultimately may lead to narrative understanding. Therefore, to study the narrative potentiality of music necessitates a focus on listening as an act in which the entire body is involved.

4 Musical Storytelling as Sonic Thinking Listening to music as a narrative can be considered a practice of sonic thinking. As I have argued throughout this essay, the play of suspense, curiosity and surprise, an interplay of tension and resolution, which make up the narrative potentiality of music,

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is experienced in the body itself as a result of the materiality of the sounds the music consists of. And this is precisely what sonic thinking entails. Sonic thinking, Cox (2017) points out, follows the flow of motions, of vibrations, of tensions and resolutions created by what we call sound and which we can feel in our bodies. At the same time, these are phenomena that are foregrounded in musical narratives. Sonic thinking, Herzogenrath (2017) asserts, is a thinking with and by means of sound, not merely a thinking about sound. Thus, sonic thinking is not primarily a reflective practice that ponders on issues such as what sound is, or can be, and what one can do with sound. Instead, sonic thinking is what Herzogenrath calls a thinking of and in the world, as sound is a part of the world we live in, intervening in the world directly. Sound has the potentiality to directly intervene in the world, because sound is vibration. Vibration, Gershon (2013) explains, is patterned oscillation. And it is this patterned movement that causes resonance. Resonance – which, as I explained above, makes up the materiality of sound – in turn, […] is theoretically and materially consequential. Theoretically, if everything vibrates, then everything — literally every object (animate and inanimate), ecology (“natural” or “constructed”), feeling, idea, ideal, process, experience, event — has the potential to affect and be affected by another aspect of everything. It is the ability of one’s self and/or not-self’s affect (object/not-object, ecology/not-ecology, etc.) to effect in a multidirectional fashion. (Gershon 2013: 258) Sound, as vibration, has the potentiality to let other things, including people and their thoughts, resonate. Thus, sound is relational in that it makes other things resonate along with it. And since everything has the potentiality to resonate, sound is able to relate to, interact with, and affect anything. As a result, Gershon proposes, “[…] if everything sings and resonates, then sound serves as both a strong theoretical site for conceptualizing what might ‘count’ as ‘data’ in qualitative research and how such methodologies might function in practice” (2013: 257). Because of its resonating qualities, sound has epistemological value, and it is this value that is exploited in sonic thinking. Interestingly, the resonating qualities of sound are also responsible for the narrative potentiality of music. The play of suspense, curiosity and surprise, the interplay of tension and resolution, which makes up this narrative potentiality, is experienced in the body as a result of resonance. Listeners literally feel this interplay in their bodies and are provoked to make sense of what they are experiencing, which in itself can already be considered a form of sonic thinking. Listening to musical sounds as a narrative implies a focus on what music can do to the bodies of listeners. It informs us about the affective capacity of music as well as how our bodies act and react as a result of being exposed to music. Put differently, musical stories articulate the fundamental embodied nature of narrative in ways that other means of storytelling, including verbal ones, cannot, and this articulation is an example of sonic thinking, in this case a thinking about the affective and embodied nature of narrative itself. Sonic thinking through musical storytelling can take place at different levels. Sonic thinking happens when listening to musical stories and trying to make sense of them, but it can also occur during the act of creating such stories. Via the creation of musical stories features of the sounds and their resulting resonances may be brought to light that

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would have remained obscured otherwise. Moreover, just as language uses rhetorical devices in order to convincingly convey an argument, this act of creation can be used as a rhetorical as well as epistemological tool to make a point sonically and musically: it is a form of sonic thinking. The epistemological potential of sonic thinking thus also lies in the explicit creation and manipulation of sounds that is necessary to turn these into musical stories. Although composing music generally cannot be equated to a conscious creation of a narrative per se, it does include acts of construction and sonic manipulation. Wolfgang Rihm, for instance, asserts that composers aim to create music that sounds logical in a musical sense: “The main task of a composer is to create something fictitious that gives the impression that it could not have been created in any other way.” (Brinkmann and Rihm 2001: 112; my translation) Moreover, this fictitious entity needs to be able to appeal to what Rihm calls “psychophysical states” (Rihm 2002: 126). What Rihm thus seems to propose is that composing is a rhetorical manipulation of sound in order to bring about particular expressive effects, a sonic exploration, a sonic thinking, that explores the manners in which such manipulations may result in the suggestion of some kind of internal musical logic. And I would add that in many cases these kinds of musical logic may be labeled as narrative.

5 Conclusion In this essay I investigated the narrative potentiality of music from an experiential point of view. Following Sternberg, I consider narrativity the act of creating an interplay of tension and resolution by exploiting suspense, curiosity, and surprise. As the expressivity of music is constituted by the interplay of tension and resolution that can be identified in the musical sounds, any music that can be considered expressive has a narrative potentiality as well. In my practice both as an improviser and a composer, I notice that I am not explicitly trying to tell a story through sounds. Obviously, I do try to express something, but what I intend to convey is a feeling of intensities, a flow of energies. Both in my improvisations and my compositions, as well as when I listen to music myself, I do not primarily focus on a larger structure as such, but instead on the movement from one sonic event to the next, and the affective energies these movements may elicit. And in order to accomplish this I need to focus on how I create an interplay of tension and resolution, an interplay that can be heard and felt in our bodies. Interestingly, despite my intentions, the resulting music may have a narrative potentiality precisely because it exhibits an interplay of tension and resolution, a potentiality that is experienced through the body, too. Listeners literally feel the interplay of tension and resolution in their bodies and are provoked to make sense of what they are experiencing, which may lead to a narrative understanding of the music, regardless of whether the music was intended as narrative or not. This thus seems to suggest that the study of the narrative potential of music necessitates a focus on listening as an act in which the entire body is involved. Finally, listening to and creating musical narratives can be considered as forms of sonic thinking. Listening to music as a narrative implies a focus on what music can do to

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the bodies and minds of listeners. It informs us about the affective capacity of music as well as about how our bodies and minds act and react as a result of being exposed to music. Likewise, performing and composing music may be regarded as acts of sonic thinking, too. These musical activities can be conceived as sonic experiments during which the expressive qualities of sounds are explored. Creating music is a thinking through and by means of sound, a thinking that may lead to new insights on the expressive and narrative possibilities of sound and music.

References Almén, B.: A Theory of Musical Narrative. Indiana University Press, Bloomington (2017) Anderson, I., Rennie, T.: Thoughts in the Field: “Self-Reflexive Narrative” in Field Recording. Organ. Sound 21(3), 222–232 (2016) Brinkmann, R., Rihm, W.: Musik nachdenken: Reinhold Brinkmann und Wolfgang Rihm im Gespräch. ConBrio Verlagsgesellschaft, Regensburg (2001) Cox, C.: Beyond representation and signification: toward a sonic materialism. J. Vis. Cult. 10(2), 145–161 (2011) Cox, C.: Sonic thought. In: Herzogenrath, B. (ed.) Sonic Thinking: A Media Philosophical Approach. pp. 99–110. Bloomsbury, New York (2017) Gallagher, S.: The narrative sense of others. HAU J. Ethnogr. Theory 7(2), 467–473 (2017) Gershon, W.S.: Vibrational affect: sound theory and practice in qualitative research. Cult. Stud. Crit. Methodol. 13(4), 257–262 (2013) Gershon, W.S.: Reverberations and reverb: sound possibilities for narrative, creativity, and critique. Qual. Inq. 0(0), 1–11 (2018) Goodman, S.: Sonic Warfare: Sound, Affect, and the Ecology of Fear. MIT Press, Cambridge (2010) Herzogenrath, B.: Sonic thinking - an introduction. In: Herzogenrath, B. (ed.) Sonic Thinking: A Media Philosophical Approach, pp. 1–22. Bloomsbury, New York (2017) Huron, D.: Sweet Anticipation: Music and the Psychology of Expectation. MIT Press, Cambridge (2006) Hydén, L.: Bodies, embodiment and stories. In: Andrews, M., Squire, C., Tamboukou, M. (eds.) Doing Narrative Research, pp. 126–141. Sage, London (2013) Kaag, J.: Thinking Through the Imagination: Aesthetics in Human Cognition. Fordham University Press, New York (2014) Livingston, P.: Narrativity and knowledge. J. Aesthet. Art Critic. 67(1), 25–36 (2009) Menary, R.: Embodied narratives. J. Conscious. Stud. 15, 63–84 (2008) Meelberg, V.: New Sounds, New Stories: Narrativity in Contemporary Music. Leiden University Press, Leiden (2006) Meelberg, V.: Sonic strokes and musical gestures: the difference between musical affect and musical emotion. In: Louhivuori, J., Eerola, T., Saarikallio, S., Himberg, T., Eerola, P-S. (eds.) Proceedings of the 7th Triennial Conference of the European Society for the Cognitive Sciences of Music (ESCOM), pp. 324–327. University of Jyväskylä, Jyväskylä (2009) Mildorf, J., Kinzel, T.: Audionarratology: prolegomena to a research paradigm exploring sound and narrative. In: Mildorf, J., Kinzel, T. (eds.) Audionarratology: Interfaces of Sound and Narrative, pp. 1–26. Walter de Gruyter, Berlin (2016) Popova, Y.: Narrativity and enaction: the social nature of literary narrative understanding. Front. Psychol. 5, 1–14 (2014) Punday, D.: Narrative Bodies: Toward a Corporeal Narratology. Palgrave, New York (2003)

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Rihm, W.: Offene Enden: Denkbewegungen um und durch Musik. Carl Hanser Verlag, München (2002) Simpson, P.: “Falling on deaf ears”: a postphenomenology of sonorous presence. Environ. Plan. A 41, 2556–2575 (2009) Sternberg, M.: Narrativity: from objectivist to functional paradigm. Poetics Today 31(3), 507–659 (2010)

The Conceptual Structure of Music: Congruence, Modularity, and the Language of Musical Thought Trevor Rawbone1,2(B) 1 Tonteg, UK 2 InnerMachines, Cardiff, UK

Abstract. This paper examines the individuation of concepts in the music faculty (MF) based on their intrinsic congruent structure (extending the theory of congruence in Rawbone (2017) and Rawbone and Jan (2020)), and explores the aggregation and chaining of concepts in a language of musical thought (LMT). It is proposed that music perception is enacted through ‘input modules’, which are components of the MF that ground basic uniparametric concepts through congruence in the realms of rhythm and pitch; these systems are innate, domainspecific, automatic, bottom-up, and informationally encapsulated. More intricate modules of the MF, here described as sub-central systems, build complex multiparametric concepts from basic concepts, generally preserving congruence and comprising a compositional syntax—constraining the LMT. The LMT can be characterised as a sequencing of causal–functional tokens of congruent conceptual representations. While the LMT is located inside the MF, it is suggested that the sub-central systems that assemble it are mediated partly by ‘central’, domaingeneral systems of thought situated outside the MF. Central systems are needed for thinking and reasoning about information that is ambiguous or noncongruent and also integrating various sources of information, such as consolidating the representations of perception and memory. There are two key considerations for the music modularity and LMT hypotheses. Firstly, determining the extent to which the grounding of multiparametrically congruent concepts is automatic, bottom-up, innate, and encapsulated and secondly, establishing why noncongruent terms are significant when there is no perceptual imperative for coining such concepts. Keywords: Language of musical thought · Modularity · Musical congruence · Music faculty · Input systems

1 Introduction This article unites three distinct theories of music perception and cognition which are argued to be mutually-supporting, or consilient: the theory of congruence, which is the thesis that low-level multiparametric features correspond and are aggregated in perception (Rawbone 2017; Rawbone and Jan 2020); perceptual modularity, which is the notion that music processing occurs in a designated music faculty (MF) (Peretz 2003, 2009); © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. D. Khannanov and R. Ruditsa (Eds.): WWMC 2021, CRSM 9, pp. 41–54, 2021. https://doi.org/10.1007/978-3-030-85886-5_4

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and the language of musical thought (LMT) hypothesis, which, building on Fodor’s (1975, 2008) theory of a language of thought, is the idea of a high-level computational musical language that processes complex concepts. Previous work indicates that while congruence shows distinct patterning across epochs and styles, it appears to be a universal constraint of perception or cognition that constrains the form of cultural features (Rawbone 2017; Rawbone and Jan 2020). In the present article, it is argued that congruence is necessary for perception to bind lowlevel features across the realms of rhythm and pitch, termed perceptual multiparametric congruence (MC). Perceptual MC supports perceptual modularity and submodularity of music processing because intrinsic MC binding from low to high levels of structure requires a designated module (i.e., the MF). However, since the MF parses only congruence at relatively low levels of structure, non-modular, domain-general central systems must be evoked to reconcile nonconcongruent percepts that emerge in higher-level structures (Fodor 1983). The language of thought hypothesis (Fodor 1975, 2008; Schneider 2011) is the idea that thought occurs in a type of mental language, or mentalese, analogous to a classical computational system, following the classical computational theory of mind (CCTM). The computational language of thought has a representational or informational conceptual content (or informational semantics), where complex concepts inherit the semantic and syntactic structure of basic concepts. In the LMT, complex concepts are chained together in strings that preserve the congruence of representational tokens. The symbolic information is processed by a syntactic engine (Fodor 2008), consistent with the CCTM. The claim that musical thought is language-like (i.e., the mind–brain uses a LMT) supports perceptual MC in a designated MF, since high-level music processing must be compositional and grounded through basic concepts but must also generalize over lower-level concepts to reduce complexity and simplify interfacing with central systems. The LMT explains how we are able to process complex terms quickly and efficiently in music listening, without access to prior knowledge or lexicons of music.

2 Perceptual Multiparametric Congruence 2.1 Basic Percepts For the perceptual MC thesis to be valid, basic pitch and rhythm percepts must be discrete categories and incorrigible to revision by cognition, which is to say they must be perceptual gestalts. That basic percepts are incorrigible enables reliable objects for higher-level combinatorial concept manipulation. It would be highly inefficient for cognition to revise basic percepts through top-down action (Fodor 1983). Pitch. The notion of a discrete pitch percept category is broadly supported across various lines of evidence. The partials that make up a periodicity pitch are often integer multiples, or harmonics of the fundamental frequency, which means that when sounded together they fuse perceptually (Bharucha 2002). Individuals with and without absolute pitch bind harmonics into pitch categories even though this category may vary between individuals and change over time (Deutsch 2013). When the fundamental frequency of a

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harmonic spectrum is removed, it is still perceived as the predominant virtual pitch (Terhardt 1979). Spectral theories (i.e., analysis of harmonics) show the grounding of pitch percepts that process harmonic content in the periphery auditory system (Helmholtz 1863) and temporal theories show the determination of pitch categories in terms of fine temporal structure (i.e., time waveform analysis) (Yost 2009; Oxenham 2012); both processes are involved in pitch perception, suggesting early unification. Also, pitch categorization occurs across a range of cultures (Savage et al. 2015). It is possible pitch percept ‘learning’ may be guided, for example, through various types of spectral pattern processing (e.g., Goldstein 1973; Terhardt 1979; Parncutt 1988; Milne 2013) or selforganizing connectionist systems, showing temporal or spectral structure (e.g., Cohen et al. 1995; Bharucha 2009; Milne 2013). In the present model, pitch is impenetrable by cognition, so high-level concepts (e.g., chords) are thought not to be learned through analysing spectral content. Indeed, complex concepts are generated innately through broadly bottom-up MC interaction in perception and cognition in real time. Rhythm. There is a diverse array of perceptual models that deal with rhythm and beat perception (Rajendran 2018). A number of key models support the primacy given to low-level regularity for basic percepts, which is argued to be significant in the present theory (see Benjamin 1984). For instance, beat perception has been modeled in terms of low-level regularity using linear filter and non-linear oscillator models (Todd 1996; Todd and Lee 2015). In computational musicology, it has been shown that regularity is at the root of metrical perception (Longuett-Higgins and Steedman 1971; Povel and Essens 1985; Rosenthal 1992).

2.2 Complex Concepts For complex music concepts to be coined by the ‘input’ system of the MF, there must be a binding of discrete pitch and rhythm information. Binding on an informational or symbolic level is needed to synthesize the disparate realms of pitch and rhythm. Perceptual MC at its most fundamental is the abstraction of regular onsets of pitch information, conjoining pitch and rhythm percepts. This occurs between low-level salient rhythmically regular units at the tactus (/beat) level and pitch categories. Complex concepts are further generated from basic and complex concepts by virtue of their MC content. This is carried out by sub-central systems, which are quasi-modular systems, in a broadly bottom-up process of abstraction based on rhythmic regularity and closeness in harmonic space (discussed in Sect. 2.4). MC concepts emerge during the unfolding of serial and parallel events in real-time. While the uptake of basic MC percepts strongly constrains structure, perception only weakly constrains higher-level concepts, so internal representation of higher-level structure can be irregular and can incorporate more distant relationships in pitch space. The notion of perceptual MC binding is broadly compatible with the binary operation ‘Merge’ for natural language syntax, espoused in the Minimalist Program (Chomsky 1995). Katz and Pesetsky (2011) adapts Minimalism to music, focusing on pitch and harmony syntax. By contrast, the current presentation considers complex hierarchical conceptual arrangements across the realms of rhythm and pitch, with mid-level conceptual types, such as textural grouping (the pattern of rhythmic

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event onsets) and harmonic rhythm (the rhythm of harmonic change), being fundamental for the unfolding of higher-level notions, such as metre (high-level rhythmic–harmonic regularity) and tonality (the multiparametric prolongation of harmony). For example, the following is a general bottom-up causal hierarchy of music perception and cognition found for Classical music listening in Rawbone (2017) (assuming rhythm is abstracted from pitch information; see Sect. 3): pitch → rhythmic grouping → pitch grouping → textural grouping → harmony → harmonic rhythm → metre → tonality. The first two abstractions are universal; at higher levels, variable real-time information also determines processing. The thesis of perceptual MC coheres with a number of important principles of music processing: an innate, bottom-up binding is necessary to comprehend non-learned infinite gradations of musical structure and permits computational efficiency for cognition; processing must be relatively automatic because deliberating about complex surface structure would involve considerable cognitive resources; perception has a shallow informational structure to process quickly and efficiently (Fodor 1983). 2.3 Rhythm and Metre A streamlined perceptual system, where rhythmic regularity is necessary for perceptual individuation, enables the efficient concretisation of rhythmic units in abstract metrical space. This process is innate and bottom-up, involving the aggregation of regular rhythmic units, generally from the tactus (/beat) level upwards. Low-level generation of regularity in perception does not place limitations of regularity at higher levels. There is an inability for perception to track non-isochronous metrical structure, even though central systems can ‘interpret’ isochronous and non-isochronous metrical and hypermetrical structures. Indeed, metrical and hypermetrical irregularity is evident in various types of music. Figure 1 shows a reduced section of J.S. Bach’s O Mensch bewein dein Sünde gross (St. Mathew Passion), showing regularity at the tactus level but irregularity (and plurality) at metrical and hypermetrical levels (the ambiguous noncongruent interacting metrical systems are shown with Arabic numerals, in grey). The noncongruent structuring suggests that the metrical and hypermetrical ‘grids’ posited in generative theories (e.g., A Generative Theory of Tonal Music, GTTM) (Lerdahl and Jackendoff 1983), may not be an actual property of perception, and may not be a property of cognition. 2.4 Chords and Harmony The harmonic perception of consonance (/congruence) can be modeled psychoacoustically in terms of the closeness of objects in pitch space (Lerdahl 2001). This scheme is broadly commensurate with theories based on alignment to the harmonic series (Rameau 1722; Schenker 1935; Krumhansl 1990; Hamanaka 2006; Marsden 2010), or which are based on spectral similarity (Parncutt 1989), harmonic affinity (Milne 2013), or maximally smooth (Cohn 1996) or efficient voice-leading (Tymoczko 2012), since restricted voice-leading movement obliquely corresponds with harmonic similarity. Pitch space can be abstractly stratified into a hierarchy of ascending order: seconds (/sevenths) space, fifths (/fourths) space, thirds (/sixths) space, and octaves (/unison) space (adapted from Lerdahl 2001). The relative salience of those spaces for building

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Fig. 1. ‘O Mensch bewein dien Sünde gross’, St. Mathew Passion, J.S. Bach, BWV 244, bb. 17–20.

tonal complexes is strongest at the top of the hierarchy and decreases with depth into the space, as shown in the following schema: octaves > fifths > thirds > seconds. Thus, octaves space supports consonant harmonic complexes more critically than fifths space, and fifths space supports harmonic complexes more critically than thirds space, and so on. This innate psychoacoustic preference for harmonic consonance in the construction of concepts partly explains the primacy of prototypical chord concepts, such as the C MAJOR CHORD or D MINOR CHORD. (Lerdahl 2013, p. 258). Figure 2 shows the basic space ‘set’ to C major (Lerdahl and Krumhansl 2007), where consonant strata are more strongly represented in the hierarchy. (Note that ‘triadic’ is replaced by thirds space in the present theory.) (a) octave (root) level: (b) fifths level: (c) triadic level: (d) diatonic level: (c) chromatic level:

(0) 0 (0) 0 7 (0) 0 4 7 11 (0) 0 2 45 7 9 0 1 2 3 4 5 6 7 8 9 10 11 (0)

Fig. 2. The basic space set to C major (Lerdahl and Krumhansl 2007).

In the present conception, in contrast to Lerdahl’s (2001) model, there is a bottom-up binding of percepts, so a top-down assumption of key is not required (see Milne 2013 on bottom-up and top-down models of harmony and tonality). This involves a selective and eliminative election of abstract pitch-space strata, where the concrete identity of pitch sets at lower levels constrains the structure of higher levels during the unfolding of events by perception in real time (although abstract higher-level pitch space strata are more harmonically perceptually salient). That is, particular abstract strata are prioritised bottom-up, through MC interaction, through the placement of pitch phenomena (corresponding with abstract strata) in rhythmically salient constellations. This involves

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unbounded modes of interaction between pitch and rhythm. The prioritisation of pitch strata can be seen in the coupling of thirds space with salient rhythmic concepts, found in late-Romantic music. Accordingly, Tymoczko’s (2012) geometry of three-dimensional pitch space enables a more coherent picture of systems with relatively salient thirds space and inhibited fifths space at high levels of structure.

3 Modularity 3.1 Evidence from Neuropsychology and Neuroscience Neuropsychologists, neuroscientists, and music theorists generally subscribe to various forms and degrees of music modularity and submodularity (Peretz 2006), sometimes positing shared systems with other capacities, such as language (Patel 2008; Lerdahl 2013; Katz and Pesetsky 2011; Deutsch 2013; Nunes–Silva and Haase 2013). In neuropsychology, many congenital or acquired amusia and aphasia cases with trauma or legions have double dissociation with respect to music and language capacities, with many amusia patients being unable to process music despite normal intellect and language (Peretz and Coltheart 2003; Peretz 2009). Dedicated music circuitry may be focused in the right hemisphere shown through acquired amusia patients with right hemisphere trauma or legions, generally in the vicinity of the auditory cortex (Peretz 2009). Indeed, Zatorre (2002) notes that a functional right primary auditory cortex is required to determine virtual pitch from harmonic complexes without fundamental pitches. The modularity thesis is supported by tonotopic (frequency to place) organisation that extends from the periphery auditory system into the primary auditory cortex. Precortical systems process a large spectrum of sounds, undertaking auditory scene analysis (Bregman 1990), examining the harmonicity of sounds, the onset synchronicity, and spatial position of objects, etc. (Deutsch 1998). Pitch category emerges in the peripheral auditory system and is extracted by the auditory cortex. Multiple tonotopic maps have been found in the human auditory cortex (Patterson et al. 2002; Tavalage et al. 2004; Norman-Haignere et al. 2015), suggesting pitch percepts are basic and categorical in the auditory cortex, and a domain where initial processing of the MF may take place. Patterson et al. (2002) shows that temporal pitch and melody information involves processing that moves anterolaterally away from the primary auditory cortex, into the superior temporal gyrus and planum polare, consistent with hierarchical concept formation. Zatorre et al. (2002) has also demonstrated that higher-level pitch processing, broadly construed as ‘pitch tracking’ and ‘melodic extraction’, are processed in distributed regions beyond the primary auditory cortex. Thus, pitch processing presumably initiates in the primary auditory cortex and radiates out into other adjacent and non-adjacent areas, which conforms to the present hierarchical model of concept formation. The perceptual grounding of basic concepts of rhythm is much less clearly understood, since rhythm processing seems to involve distributed cortical activity in the brain, including the premotor cortex (Rajendran et al. 2018). Prima facie, this amounts to an extremely complex picture of rhythm perception and music perception generally. However, widespread cortical activity may not contribute to the individuation of rhythmic percepts in the MF. Rather, the rhythmic structure of a pitch sequence may be abstracted from that sequence, in the auditory cortex, as has been theorised in Todd (1996) and

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suggested in Griffiths and Frakowiak (1998). Recent work in neuroscience on human and animal rhythm processing has found the representation of beat in the auditory cortex (Rajendran et al. 2020). Thus, this streamlining of rhythm perception—where rhythmic information is abstracted from pitch percepts in the same domain—is feasible, elegant, and efficient for music perception, meaning pitch–rhythm percepts and their complexes do not require re-synthesis in cognition. More broadly, while neuroscience shows us that music processing in general recruits large parts of the brain’s circuitry in both hemispheres (Peretz and Zatorre 2005), this may not necessarily be contrary to the modularity thesis. Modularity can co-exist with various forms of domain-general central systems (Schneider 2011), which accounts for the widespread cortical activity. 3.2 Schemas of Music Modularity Peretz and Coltheart (2003) present a schematic model of music modularity that depicts distinct systems for pitch and rhythm processing (see also Lerdahl 2013, pg. 271) and a separate system for natural language processing (Fig. 3). Patel (2008) and Lerdahl (2013) posit shared rhythm and metrical systems for language and music. This is unlikely from the present perspective, since in the theory of perceptual MC rhythm and pitch are bound early and intrinsically in the MF.

Fig. 3. Schematic model of music modularity in Peretz and Coltheart (2003).

Peretz and Coltheart (2003) and Lerdahl (2013) argue that pitch contour is processed prior to fixed pitch relations in perception, through gestalt principles. This is feasible prima facie because pitch contour gestalts seem to be automatically determined precortically as part of general auditory scene analysis. However, contour ‘gestalts’ are not fundamental for perceptual MC, although contour may be significant in its interaction with other features. Indeed, contour does not interact necessarily with essential mid-level conceptual parameters, such as textural grouping and harmonic rhythm (for deeper discussion of these conceptual categories, see Swain (2002)). The complex metrical event

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hierarchies in generative theories are implausible since they posit a direct connection between grouping gestalts and ‘metre’. As discussed in Sect. 2.3, the notion of high-level, grid-like metre is a questionable construct because highly non-isochronous structures abound in various styles, suggesting that metre is not represented in perception, and may not be represented in cognition. To reconsider the point made in Sect. 2.3 with regard to Fig. 1, textural grouping is often highly irregular in many musical periods and styles (such as those of the Renaissance and Baroque), informing non-isochronous metrical and hypermetrical structures (Rawbone and Jan 2020). Grouping by pitch contour gestalts and the separation of pitch and rhythm would involve the abstraction of separate event hierarchies, which is problematical because such would require reassembling higher up in cognition, and so would be highly inefficient and expensive in cognitive resources. This reasoning can be applied also, mutatis mutandis, to other musical notions, such as intervalic information, pitch height, and scales, etc. If these are processed perceptually they must later be recombined higher up in the conceptual apparatus, resulting in considerable inefficiency. Thus, generative theories (Lerdahl and Jackendoff 1983; Temperley 2001; London 2004; Hamanaka et al. 2006; Rohrmeier 2011) are broadly unfeasible because they endorse conceptual reconstitution of theoretical components or event hierarchies, such as grouping hierarchies, metrical hierarchies, and time-span reductions. The Peretz and Coltheart (2003) model (Fig. 3) posits the idea of a music lexicon. However, music has a graded conceptual structure, so a bank of lexical terms (e.g., chords) would demand large memory resources and processing power to enable ‘concept recognition’. A main motivation against a musical lexicon may be termed the extreme poverty of the stimulus argument. This is an analogue of Chomsky’s (1966) poverty of the stimulus argument for natural language, which is the thesis that the exposure to correct language use in childhood is inadequate to supply speakers with observed combinatorial complexity, so language must presumably be an innate capacity. In music, the problem of poverty of exposure is even more pronounced, since musical concepts are sliced thinner than words, and the grammar more intricate. This nominalist position—where congruent concepts, such as common chords, are abstractions that are inconsistently locked in perception and reconstructed independently on each presentation—is also a solipsistic picture of music processing, since from this perspective, perceptually, concepts are not shared between minds. This may be an unsatisfactory position because canonical music theoretical ideas, including chords, scales, and intervals, are decoupled from perceptual reality. Nevertheless, this stance enables the MF to provide cognition with a faithful presentation of the non-essentialist and unbounded musical landscape. Figure 4 shows a schematic view of music processing that involves perceptual MC and a shallow modular and submodular architecture. Systems that comprise both pitch and rhythm are in green; pitch-only, rhythm-only, and general systems are in blue. The broad direction of mapping is bottom-up, from acoustic input, to the hearing faculty, to the input system, to sub-central systems, and to central systems. The hearing faculty includes both the peripheral hearing system and auditory cortex, grounding basic concepts of pitch through spectral and temporal information. The MF contains the music input system, which binds basic and rhythm percepts, as well as sub-central systems, which rapidly parse chains of complex congruent concepts, generating a LMT. While

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relatively automatic, the sub-central systems are informationally unencapsulated, being mediated by central systems. The domain-general central systems, while intrinsically opaque, are assumed to interact with each other and engage in bottom-up and top-down interaction with sub-central systems.

Fig. 4. Schematic diagram of music processing showing the music faculty and central systems.

4 Perception and Cognition 4.1 The Language of Musical Thought Functionalism. A higher-level musical language, the LMT, is required to manipulate highly complex concepts while inheriting the semantic and syntactic structure of more primitive concepts. This involves a form of psychological functionalism, where terms are abstract symbols that are manipulated by a computational syntax. While the LMT is compositional and productive—meaning complex structures can be generated from basic terms—it is not necessarily systematic, as has been suggested for natural language (Chomsky 2009), since musical syntax is more variable and idiosyncratic. As outlined above, the LMT takes place in sub-central systems situated in the MF. Subcentral systems are similar to input systems, being domain-specific, neurally-specific, and broadly innate, but unlike input systems in that they are not exclusively bottom-up and are not informationally encapsulated, since they receive top-down information from domain-general central systems. The LMT chains complex pitch-rhythm concepts in short-term memory, preserving congruence through combining concepts in terms of regular rhythmic structure and harmonic proximity in pitch space. Broadly analogous to the truth functions of classical

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propositional logic, which are truth-preserving, the language of functional complex concepts preserves congruence between conceptual terms, and so is congruence-preserving. This enables the establishment of musical beliefs higher up in central systems. Indeed, the preservation of congruence between terms permits the possibility of a coherent representation of musical structure for central systems. Figure 5 illustrates a section of Beethoven’s Sonata, Op. 2, no. 3, involving a highly congruent string in the LMT. Functional terms can be parsed from left to right, involving complex hierarchically arranged concepts (shown with rectangular boxes), with regular textural grouping (hemispheres), regular harmonic rhythm (four-part ratio), and chords ‘close’ in fifths space (one step). Thus, although not formalised here, each pitch–rhythm complex functional term would preserve congruence, allowing in this case such notions as hypermeter and tonality to be formed at higher levels, in central systems.

Fig. 5. Pitch-rhythm congruence-preserving structure in Beethoven’s Sonata, Op. 2, no. 3 (1795)

Sub-central systems cannot parse terms that are noncongruent within the context of a congruent string, so when a noncongruent term is encountered in such a context, the generative process must be reiterated to form a new string. Figure 6 shows a reduced section (vocal melody and guitar chords) of Nirvana’s Drain You (1991), with functional chaining of interlocking congruent strings (shown with brackets). However, the strings are collectively noncongruent in pitch space: there is no overarching key and only a weak hypermetrical hierarchy (despite regular textural grouping and harmonic rhythm). Any of the roots of all the ‘power chords’ (which omit the thirds of conventional chords) may be construed as tonal centres (A, C-sharp, F-sharp, or B), because the chordal loop and vocal melody give rise to multiple conflicting relationships in pitch space. The strings, which correspond abstractly with fifths, thirds, and seconds spaces, conflict with each other; each space ‘eliminates’ the other at higher levels (see Sect. 2.4). The use of conflicting (/noncongruent) relationships between pitch space strata means there is a weak or incoherent pitch space hierarchy (diverging from the schema in Sect. 2.4), and thus tonal and (hyper)metrical ambiguity. Since the sub-central systems cannot parse the section wholly, generating separate interlocking strings, the noncongruent structures must be synthesised in central systems. The psychological functionalism in the LMT is distinct from classical Riemannian (1905) harmonic functionalism, since the symbolic language of the LMT preserves the binding between pitch and rhythm in the constituent MC concepts when preserving the content of symbols. Invoking a belief–desire psychology contrasts with various theories of music that posit information-theoretic or associative–statistical explanations of musical meaning (cf. Meyer 1956; Conklin and Witten 1995; Pearce and Wiggins 2012;

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Fig. 6. Interlocking pitch–rhythm functional strings in Nirvana’s Drain You (1991).

Hansen and Pearce 2014; Dhariwal et al. 2021). Such ‘empiricist’ theories, based on associative–statistical enumeration of musical structure, are arguably unable to model the complex interaction of conceptual hierarchies and combinatorial concept manipulation in the higher-level LMT. Multiple Languages. Fodor (1975) discusses the possibility of multiple languages of thought operating simultaneously in the mind–brain. This may be the case with music, which seems to involve distinct, although interacting, functional entities, such as the interacting complexes of melody and accompaniment or interacting voices in counterpoint. In melody, for instance, there can be hierarchically arranged complex constituent concepts locked within its structure, such as harmonic rhythm, textural rhythm, etc. This suggests a highly complex picture of music processing, where interacting functional languages require unraveling in the mind–brain, presumably in central systems. When these languages are combined in central systems this may lead to ambiguous or even incoherent beliefs about musical structure that require reconciliation. To return again to Fig. 1, it can be seen that there are two distinct functional languages operating interdependently and with separately individuated conceptual terms. The melody language has distinct tonal structure (shown in grey), harmonic structure, harmonic rhythm, and textural grouping components from those of the accompaniment language. Perceptual Content of the LMT. The functionalism of the LMT contrasts to an extent with the picture of cognition espoused in generative theories, but conforms to a number of key general requirements for perceptual efficiency, such as shallowness and automaticity (Fodor 1983). These are significant because the perceptual content of music has been shown to involve the complex nesting of constituent percepts in music hierarchies (such as harmonic rhythm, textural grouping, etc.). It is unfeasible that such complexity is fully tractable by higher-level cognitive systems. Rather, lower-level concepts must be generalized in the higher-level language. The idea of independent event hierarchies that are synthesised in cognition (e.g., melodic grouping, time-span reductions, etc., in GTTM) is an unfeasible picture of music processing.

4.2 Central Systems Central systems are needed to preside over the work carried out in the sub-central systems: directing attention to particular perceptual systems, consolidating interacting functional entities, and providing continuity to bottom-up perception. Indeed, while bottom-up conceptual structure culminates in one or more functional languages, central

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systems act in a bottom-up and top-down fashion to form beliefs about musical structure. In the process of individuating congruent percepts, higher-level noncongruences emerge (e.g., irregular hypermetre, polytonality, etc.); these require resolution in central systems through some form of re-representation to fix belief, the nature of which is currently opaque. Likewise, and discussed in connection with Fig. 1, the two interacting languages and their component concepts—e.g., chord structures, textural groupings, and harmonic rhythms—require mediation by central systems. Central systems also permit connections between perceptual content and musical and non-musical long-term memory, and coordinate musical information with the body and emotions. Perhaps most importantly, central systems may serve as a useful notion towards an explanation of creativity, although this is something that remains poorly understood.

5 Findings and Discussion This article has posited a shallow, bottom-up perceptual modularity and sub-modularity of music, involving the MC binding of low-level pitch and rhythm percepts. The complex hierarchical MC binding of percepts requires a dedicated MF, which comprises an innate bottom-up input system and quasi-modular sub-central systems. A functional, belief– desire psychology permits the chaining of MC concepts in a LMT, required to generalize over constituent terms. The LMT comprises computation that preserves the congruence of concepts, enabling a contiguous belief system higher up in central systems. Central systems reconcile noncongruent concepts that emerge in the LMT to construct complex beliefs about music. Many music theory and computational musicology models—and also psychological and neuroscientific studies of music—isolate the realms of pitch and rhythm, which can yield incoherent explanations of music processing. ‘Rationalist’ generative theories (Rohrmeier 2011; Hamanaka et al. 2006; London 2004; Temperley 2001; GTTM) construe monolithic tension representations that do not observe the rich, differentiated, and unbounded perceptual and conceptual structure. Similarly, ‘empiricist’ statistical theories in music theory (e.g., Meyer 1956; Gjerdingen 1988), music psychology (e.g., Huron 2006), and computational musicology (e.g., Conklin and Witten 1995; Hansen and Pearce 2014, Dhariwal et al. 2021) do not explain the fine-grained conceptual hierarchies involved in music processing. Such approaches often posit fixed statistical–associative style regularities, extracted from surface structure, or develop notions of meaning, style, affect, or creativity using information-theoretic metrics (Pearce and Wiggins 2012). Significantly, these cannot account for the generation of hierarchical and combinatorial MC conceptual structure. Further work is required to explore the interaction of multiparametric features to model the generation and processing of congruent and noncongruent musical structure.

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Bharucha, J.: From frequency to pitch, and from pitch class to musical key: shared principles of learning and perception. Connect. Sci. 21(2–3), 177–192 (2009) Bregman, A.: Auditory Scene Analysis. MIT Press, Cambridge (1990) Chomsky, N.: Cartesian Linguistics: A Chapter in the History of Rationalist Thought. Cambridge University Press, Cambridge (2009 (1966)) Chomsky, N.: The Minimalist Program. MIT Press, Cambridge (1995) Cohn, R.: Maximally smooth cycles, hexatonic systems, and the analysis of late-romantic triadic progressions. Music Anal. 15(1), 9–40 (1996) Cohen, M., Grossberg, S., Wise, L.: A spectral model of pitch perception. J. Acoust. Soc. Am. 98, 862–879 (1995) Conklin, D., Witten, I.: Multiple viewpoint systems for music prediction. J. New Music Res. 24(1), 51–73 (1995) Dhariwal, P., Jun, H., Payne, C., Kim, J., Radford, A., Sutskever, I.: JukeBox: a generative model of music, OpenAI. https://www.openai.com/blog/jukebox. Accessed 08 May 2021 Deutsch, D.: The Psychology of Hearing. Sound & Video Contractor (1998) Deutsch, D.: Absolute Pitch. The Psychology of Music. Academic Press (2013) Fodor, J.: The Language of Thought. Harvard University Press, Cambridge (1975) Fodor, J.: The Modularity of Mind: An Essay on Faculty Psychology. MIT Press, Cambridge (1983) Fodor, J.: LOT 2: The Language of Thought Revisited. Oxford University Press, Oxford (2008) Griffiths, T., Frackowiak, R.: Analysis of temporal structure by the human brain. Nat. Neurosci. 1(5), 422–427 (1998) Gjerdingen, R.: A Classic Turn of Phrase: Music and the Psychology of Convention. University of Pennsylvania Press, PA (1988) Goldstein, J.L.: An optimum processor theory for the central formation of the pitch of complex tones. J. Acoust. Soc. Am. 54, 1496–1516 (1973) Hamanaka, M., Tirata, K., Tojo, S.: Implementing “a generative theory of tonal music.” J. New Music Res. 35, 249–277 (2006) Hansen, N., Pearce, M.: Predictive uncertainty in auditory sequence processing. Front. Psychol. 1, 1–17 (2014) Helmholtz, L.F.: On the Sensations of Tone as a Physiological Basis for the Theory of Music, 4th edn. Ellis, A.J. (Trans.) Longmans, Green, and Co., New York (1863) (1912) Huron, D.: Sweet Anticipation: Music and the Psychology of Expectation. MIT Press, Cambridge (2006) Katz, J., Pesetsky, D.: The identity thesis for language and music, unpublished manuscript (2011) Krumhansl, C.: Cognitive Foundations of Musical Pitch. Oxford University Press, Oxford (1990) Lerdahl, F.: Tonal Pitch Space. Oxford University Press, Oxford (2001) Lerdahl, F.: Musical syntax and its relation to linguistic syntax. In: Arbib, M. (ed.) Language, Music, and the Brain: A Mysterious Relationship. MIT Press, Cambridge (2013) Lerdahl, F., Jackendoff, R.: A Generative Theory of Tonal Music. MIT Press, Cambridge (1983) Lerdahl, F., Krumhansl, C.: Modeling tonal tension. Music Percept. 24(4), 329–366 (2007) London, J.: Hearing in Time: Psychological Aspects of Musical Meter. Oxford University Press, Oxford (2004) Longuet-Higgins, C., Steedman, M.: On interpreting Bach. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence 6, pp. 221–241. Edinburgh University Press, Edinburgh (1971) Marsden, A.: Schenkerian analysis by computer: a proof of concept. J. New Music. Res. 39(3), 269–289 (2010) Meyer, L.: Emotion and Meaning in Music. University of Chicago Press, Chicago (1956) Milne, A.: A computational model of the cognition of tonality, Doctoral thesis. The Open University, UK (2013) Norman-Haignere, Kanwisher, N., McDermott, J.: Distinct cortical pathways for music and speech revealed by hypothesis-free voxel decomposition. Neuron 88, 1281–1296 (2015)

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Nunes-Silva, M., Haase, V.: Amusias and modularity of music processing. Psychol. Neurosci. 6(1), 45–56 (2013) Oxenham, A.: Pitch perception. J. Neurosci. 32(39), 13335–13338 (2012) Parncutt, R.: Revision of Terhardt’s psychoacoustic model of the root(s) of a musical chord. Music Percept. 6(1), 65–94 (1988) Patel, A.: Music, Language, and the Brain. Oxford University Press, Oxford (2008) Patterson, R., Uppenkamp, S., Johnsrude, I., Griffiths, T.: The processing of temporal pitch and melody information in auditory cortex. Neuron 36, 767–776 (2002) Pearce, M., Wiggins, G.: Auditory expectation: the information dynamics of music perception and cognition. Top. Cogn. Sci. 4, 625–652 (2012) Peretz, I.: The nature of music from a biological perspective. Cognition 100, 1–32 (2006) Peretz, I.: Music, language and modularity framed in action. Pscyhologica Belgica 49(2 & 3), 157–175 (2009) Peretz, I., Coltheart, M.: Modularity of music processing. Nat. Neurosci. 6(7), 688–691 (2003) Peretz, I., Zatorre, R.: Brain organization for music processing. Annu. Rev. Psychol. 56, 89–114 (2005) Povel, D., Essens, P.: Perception of temporal patterns. Music Percept. 2, 411–440 (1985) Rajendran, V., Teki, S., Schnupp, J.: Temporal processes in audition: insights from music. Neuroscience 389, 4–18 (2018) Rajendran, V., Harper, N., Schnupp, J.: Auditory cortical representation of music favours the perceived beat. Roy. Soc. Open Sci. 7, 1–13 (2020) Rameau, J.: Treatise on Harmony. Dover Publications, US (1971 (1722)) Rawbone, T.: The butterfly schema as a product of the tendency for congruence and hierarchical selection in the instrumental musical grammar of the classical period, Doctoral thesis. University of Huddersfield, UK (2017) Rawbone, T., Jan, S.: The butterfly schema in the classical style: a product of the tendency for congruence. Music Anal. 39(1), 85–127 (2020) Riemann, H.: Grundriß der kompositionslehre, 3rd edn. Max Hesse, Leipzig (1905) Rohrmeier, M.: Towards a generative syntax of tonal harmony. J. Math. Music 5(1), 35–53 (2011) Rosenthal, D.: Emulation of human rhythm perception. Comput. Music J. 16(1), 64–76 (1992) Savage, P., Brown, S., Sakai, E., Currie, T.: Statistical universals reveal the structures and functions of human music. Proc. Natl. Acad. Sci. U.S.A. 112(29), 8987–8992 (2015) Schenker, H.: Free composition. Oster E. (tr.), Longman, New York (1979 (1935)) Schneider, S.: The Language of Thought: A New Philosophical Direction. The MIT Press, Cambridge (2011) Swain, J.: Harmonic Rhythm: Analysis and Interpretation. Oxford University Press, Oxford (2002) Tavalage, T., Sereno, M., Melcher, J., Ledden, P., Rosen, B., Dale, A.: Tonotopic organization revealed in human auditory cortex revealed by progressions of frequency sensitivity. J. Neuropsychol. 91, 1282–1296 (2004) Temperley, D.: The Cognition of Basic Musical Structures. MIT Press, Cambridge (2001) Terhardt, E.: Calculating virtual pitch. Hear. Res. 1, 155–182 (1979) Todd, N.: Towards a theory of the principle monaural pathway: pitch, time and auditory grouping. In: Proceedings of the Workshop on the Auditory Basis of Speech Perception, pp. 216–221 (1996) Todd, N., Lee, C.: The sensory motor theory of rhythm and beat induction 20 years on: a new synthesis and future perspectives. Front. Hum. Neurosci. 9, 1–25 (2015) Tymoczko, D.: The Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. Oxford University Press, Oxford (2012) Yost, W.: Pitch perception. Atten. Percept. Psychophys. 71(8), 1701–1715 (2009) Zatorre, R., Berlin, P., Penhume, V.: Structure and function of auditory cortex. Trends Cogn. Sci. 6(1), 37–46 (2002)

Evolution and Perception

Correlations Between Musical and Biological Variation in Derivative Analysis Carlos Almada(B) Federal University of Rio de Janeiro, Rio de Janeiro, Brazil [email protected]

Abstract. This paper introduces the basic structure of an original systematic model for derivative analysis (MDA). The study describes some correlations between musical and biological variation (especially in an evolutionary sense) that are explored in MDA. This involves not only metaphorical associations, but also more concrete aspects, that are reflected in adopted premises, conceptualization, terminology, and methodology. The use of these elements contributes for improving the systematization of the procedures in the model. Consequently, it helps to reduce the margin of subjectivity that is inherent in derivative analysis. Keywords: Musical and Biological Variation · Evolution · Model of Derivative Analysis · Developing Variation and Grundgestalt

1 Introduction In his The Origins of Species, published in 1859 [1], Charles Darwin attributes to variation the role of main propelling force in the creation of life diversity. According to his theory, geographic isolation of a given population (due to any cause, as natural disasters, for example), may provoke adaptive pressures that in due time lead to variations and, in very longer periods, to further speciation (i.e., formation of a new specie).1 Darwin’s insightful findings about variation (and selection) established the basis for the twentiethcentury genetic revolution that allowed the uncovering of structures (genes, DNA, RNA, nucleotides, etc.) and processes (chromosome replication, protein synthesis, etc.) that ultimately led scientists to genome mappings, among other amazing achievements.2 In recent times, metaphorical relations with biological derivation have been explored by theoretical, analytical, and compositional studies centered on musical variation. Dora Hanninen [3] searches for connections between species concepts and associative sets in music, focusing especially on the correspondences between phylogenetic 1 It is worth to say that the concept “speciation” was not coined by Darwin himself, but only

60 years after the publication of The Origins of the Species by the efforts of scientists like T. H. Morgan, H. J. Muller, R. A. Fisher, J. B. S. Haldane, and Sewall Wright, according to Ernst Mayr. For more information about speciation, see [2] (192–206). 2 Referring to all new discoveries made in this field along the last decades, Ernst Mayr highlights the fact that “[u]nexpectedly, the basic Darwinian concepts of variation and selection were not affected in any way” [2] (124). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. D. Khannanov and R. Ruditsa (Eds.): WWMC 2021, CRSM 9, pp. 57–67, 2021. https://doi.org/10.1007/978-3-030-85886-5_5

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relations and associative lineages observed in analyses of some musical excerpts (by Stravinsky, Messiaen, and Feldman), established by contextual conditions. James Benett [4] bases his study on Bartók’s writings and lectures about an evolutionary view of his own music, considering especially its folk origins, related by the composer to a natural growth similar to species evolving. Benett adopts a transformational-phylogenetic approach in analyses of some of Bartók’s compositions, combining Hanninen’s trees [3] with David Lewin’s graphs [5]. Anthony Burton [6] proposes a hybrid system combining the ideas of genetic algorithms and neural networks for composition of multi-voice percussive pieces. His ART neural network is used as an evolutionary evaluator, by the adoption of fitness parameters. Patrick Donnelly and John Sheppard [7] propose a genetic algorithm able to evolve a composition from a single chord, by using fitness functions and mutational rules, named by them as “genetic operators”. Vsevolod Arutyunov and Alexey Aberbink [8] introduce their “Genom software platform”, used for creation of variations from a given referential melody by the use of genetic-algorithm strategies, as crossover, fitness functions, and a number of mutational operators (affecting rhythm, adding ornament, etc.). Genom has an interface that allows a user to set the desired transformations to be applied. Additionally to these ones, many other compositional researches using evolutionary approaches have been pursued in the recent years, as exemplified in [9, 10], and [11]. The present paper has as the main goal to introduce an analytical model for musical variation that uses a group of concepts borrowed from the field of biological-evolutionary variation. This Model of Derivative Analysis (identified by the acronym MDA) comprises a consolidated set of premises, concepts, special symbology/nomenclature, and methodological tools (including computational ones).3 The next sections describe some of MDA’s elements that are directly associated with biological issues. Such associations contribute to enhance the intended systematization of the analytical processes.

2 The Model of Derivative Analysis In its current format, MDA addresses musical variation under two basic approaches: (a) as an isolated, abstract sort of algebraic transformation; and (b) considering a musical context, that is, taking into account the temporal dimension. Such a treatment is primarily intended to contribute to decrease the inherent margin of subjectivity in motivic-thematic analyses that naturally arise from the multiplicity of possible ways in which motives can be transformed and related to each other in a given musical passage. MDA addresses the root of this problem by adopting as premise that an isolated musical idea can be decomposed into basic components (pitches, durations, harmonic context, etc.). These, in turn, can be manipulated in different ways (for example, obtaining pitch classes, intervals, or an abstract melodic contour from a sequence of pitches), which are then algebraically described and combined in a matrix format. Figure 1 summarizes these

3 For studies on theoretical aspects related to MDA, see [12, 13]. For one of its analytical

applications, see [14]. For a study associated with MDA’s compositional approach, see [15].

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stages with a very simple example, in this case considering only pitch and rhythmic domains.4

Fig. 1. Decomposition of motive a into pitch (a.p) and rhythmic components (a.r). Both provide distinct algebraic descriptions (attributes) that are then inserted into the matrix of attributes of a (Ma ).

3 MDA’s Biological Correspondences Matrices of attributes become precise multi-dimensional descriptors of musical units in derivative analysis, providing a systematic basis for evaluation and quantification of similarity relations with possible variants, through edit-distance algorithms.5 In a metaphorical sense, it is possible to associate the structure and content of the matrix with the biological notion of genome. An isolated element of an attribute could be thus broadly considered as a kind of “allele” inside a “locus” (the respective cell of the 4 As one can observe, the matrix of attributes of the example has five columns, corresponding

to the cardinality (number of events) of the motive. The number of rows of M depends on the number of domains (here only two, pitch and rhythm) and attributes considered (nine, in the case). Since p3 and t2 deal with differences, the last cells of the respective rows (shaded in the figure) are occupied by the one-element attributes, respectively, p4 and t3. 5 For limitation of space, this aspect will not be treated in the paper.

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matrix). Pursuing this line of reasoning, a “concrete” musical unit (the original motive from which were extracted the decomposable elements) can be seen as the “phenotypic” expression of its “genes”. The main purpose of this paper is to address other associations like this, that are, in lesser or greater extent, present in MDA and that ultimately contribute to the systematization of the analytical processes. 3.1 Decontextualized Variation An important distinctive aspect in the model is the possibility of analyzing variations as algebraic transformations applied to isolated portions of the “genome” of a musical idea. Figure 2 provides a simple illustration of this, through the comparison of the motive a of Fig. 1 with a variant of it, obtained through intervallic inversion (an operation denoted by the symbol “I”). The transformation can be considered in two levels: high (or “phenotypic”), or low (“genetic”), in this case corresponding to a multiplication of the third row of the matrix (assigned to attribute p3) by -1. Observe that while some elements are not affected at all by the variation (the rhythmic attributes, in gray), others (p1, p2, p4, and p5) suffer only “collateral effects” from the main, intervallic transformation.

Fig. 2. Derivative analysis of motive a1 , considering it as a high-level inversion of a. Both matrices of attributes involved are detailed, indicating the low-level transformation suffered in attribute p3

Another possibility that expands largely MDA’s capacity for capturing more subtle modifications of an original material is the idea of “mutational” transformations. Instead of affecting an entire attribute (as in the example of Fig. 2), “mutational” variation can be applied to a single “locus” (or a limited portion of the attribute). Like biological mutations, this analytical strategy is very useful to deal with minimal variations (frequently accumulating with others) that have structural consequences in a piece.6 6 If we disregard the enormous differences of the time scales involved, this would be metaphor-

ically compared to mutations that lead a species to improve their chances of survival and, therefore, are selected. In a similar sense here intended to music, see a computational experiment proposed by Richard Dawkins (in his case, using geometric figures for representing life beings) that attempts to reproduce along a number of generations how accumulated mutations can produce extreme divergence [18] (52–91).

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Using the same referential unit a, Fig. 3 provides an example of a “mutational” transformation, considering now the rhythmic domain.7

Fig. 3. Derivative analysis of motive a2 , considering it as a high-level mutational diminution of a. Both matrices of attributes involved are detailed, indicating the low-level transformation suffered in the second “gene” of attribute t1.

3.2 Variation on Time Eventually, when contextualized, variation assumes a multidimensional and very dynamic role, especially if developing variation techniques are applied. Concisely, this Arnold Schoenberg’s concept refers to the recursive use of variation over variation, which may lead to the production of a vast amount of motivic material (even very remote units) from a basic source (or Grundgestalt, another principle coined by Schoenberg).8 Due to its inherent expansive nature and the potential growth power it has, developing variation (which we could also name as “variation across time”) is not easy to be detected and systematically mapped in analysis of real music. MDA addresses this task adopting a number of assumptions, concepts, and strategies, some of them borrowed from evolutionary biology, with which keeps some metaphorical relations of similarity. This section intends to list and describe the functionality of these elements inside the model. 7 As shown in the example, the application of a mutational operation in MDA is denoted by an

asterisk at the side of its identification. 8 Besides Schoenberg’s own writings (see, for example, [19] and [20]), there is a vast literature

related to different aspects of the two principles. Walter Frisch presents an in-depth analysis of Brahms’s use of developing variation along his career, identifying some important compositional techniques [21]. Patricia Carpenter proposes an original approach related to harmonic-functional implications of the Grundgestalt of Beethoven’s Sonata op.57, contributing with a more abstract interpretation of this concept [22]. Ethan Haimo discusses the presence of developing variation in Schoenberg’s serial music, arguing that twelve-tone procedures are in fact subordinated to the motivic treatment [23]. Bryan Simms extends a similar approach to Schoenberg’s atonal period [24]. Jack Boss, who studies symmetry in Schoenberg’s serial composition, presents a comprehensive discussion about the philosophical roots of the principles of Grundgestalt and developing variation in the light of Schoenberg’s understanding of the musical idea [25].

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Fig. 4. General representation of an intermediary hypothetical stage between two related musical units (a); an example with five ihs mutational transformations as analytical explanation for a derivation (b).

An intermediary hypothetical stage (ihs) refers to a possible musical idea (not actually present in the score) or a chain of transformations that hypothetically could connect a referential unit to one of its variants. It is an analytical construct that aims to contributes to turn more parsimonious (in derivative terms) the linkage between two related forms, corresponding metaphorically to a “lost” (or not yet uncovered) fossil record

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that could better explain the gradual derivation of a species. Figure 4 provides a general representation of this situation and a hypothetical example. Both high- and low-level derivations are considered in developing variation, being approximately associated with evolutionary processes related to, respectively, populations and genes. A “genealogical” notation intends to systematically identify lineages of variants in both levels. The label assigned to a given variant informs its derivative provenance, as well as the generation it is associated with, as a sort of a precise “address” of derivation. The notation system is quite simple: 1. Define a head as a referential, initial unit by using a lowercase letter in the alphabetic normal order (a, b, c, …) in the case of a “population” (a motive-form), or a uppercase letter in the reverse alphabetic order (Z, Y, X, …) in the case of a “gene” (i.e., a meaningful attribute). In both situations a “zero” is subscripted to the letter denoting its quality of epicenter of the derivative processes; 2. Variants of first order (i.e., direct transformations of the head) are indicated as subscript numbers at the right of the corresponding letter (ex: a1 , Z3 , etc.); 3. Variants of second and higher order (i.e., derived from variants) are also labeled with subscripted order numbers after separating dots. The number of dots ultimately denotes the generation to which the variant belongs (ex: a1.2.1 , X2.1.1.3 , etc.).9 In the case of high-level lineages, the variants referred to a given head integrate a “species”. The accumulated variations may eventually lead the analyst to consider that a “speciation” takes place. In this case, a new head is assigned, inaugurating its own lineage. Low-level lineages considered in MDA, like real genetic variation, develop in a quite different logic as a “long-term” process: the head tends to maintain indefinitely its “control” over its “offspring”, no matter the accumulation of transformations. In MDA’s analyses, both processes are mapped and plotted as phylogenetic-like trees (similar to those used in [2] and [3]). Figure 5 illustrates this with partial results of a derivative analysis of Brahms’s Piano Intermezzo op. 118/2. The graphs provide an overview of high- and low-level derivative relations detected in the section A of the piece (mm.1–16). The upper tree depicts the beginning of the evolutionary process of “species” a, trigged by the Intermezzo’s Grundgestalt, represented by the head a0 . The lower tree maps the derivation of the “gene” Z that isolates the diatonic intervallic sequence from the Grundgestalt (labelled as “d-p3” in the figure).10 9 In order to simplify the labelling of the strings, number repetitions longer than three are replaced

by the corresponding exponents, for instance, the label b2.1.1.1.1.3 becomes b2 .1 3.3 . 10 Unlike attribute p3 that is calibrated in semitones, d-p3 refers to scalar degrees of a given key. Observe also that in spite of the piece is written in A major, by convention, intervallic sequences in MDA are always transposed to C in order to provide a more neutral and standardized representation.

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Fig. 5. High- and low-level phylogenetic trees of the main section of Brahms’s Intermezzo op. 118/2 (mm. 1–16). Dotted arrows indicate possible associative relations.

Fig. 6. Phylogenetic tree related to high-level derivative analysis, encompassing the whole intermezzo. Nodes represent “population” variants. Gray nodes indicate “speciation”. The eight formal segments considered in the analysis correspond to the areas in the figure (forming “ecological niches”).

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More abstract versions of the two graphs, focused on the relations between the involved units, are also provided by the analytical model. Figure 6 depicts a global view of the derivative analysis of the Intermezzo, covering the entire piece (it was segmented in eight sections of derivative interest, matching approximately the main formal boundaries). As suggested in the scheme, three “species” (a, b, and c)11 with the respective variants seem act mostly inside these segments, like “ecological niches”, which brings another interesting metaphorical connection with evolutionary phenomena.

4 Concluding Remarks This article addressed the co-relations that exist between biological and musical variation by describing some concepts and strategies adopted in an original model used for derivative analysis of organically-constructed pieces. More than good metaphors used for making palatable the understanding of the model’s elements, premises, and mechanisms, these links contribute decisively to increase the systematization of the methodology, turning the analytical processes more objective and accurate. Practical applications (like the analysis of Brahms’s op. 118/2) are currently in process. Future studies will address additional computational implementation of the system in order to expand the automatized part of the analysis.

References 1. Darwin, C.: On the Origin of Species, 1st edn. John Murray, London (1859) 2. Mayr, E.: What Evolution Is. 2nd edn. Phoenix, London (2002) 3. Hanninen, D.: Orientation, criteria, segments: a general theory of segmentation for music analysis. J. Music Theory 45(2), 345–433 (2001) 4. Benett, J.: Explosion of Diversity: Béla Bartók’s Evolutionary Model of Folk Music. Diss. (PhD in Philosophy), University of Wiscosin, Madison (2015) 5. Lewin, D.: Generalized Musical Intervals and Transformations, 1st edn. Yale University Press, New Haven (1987) 6. Burton, A.: Hybrid neuro genetic pattern evolution system applied to musical composition. Diss. (PhD in Electronic Engineering). University of Surrey, Guildford (1998) 7. Donnelly, P., Sheppard, J.: Evolving four-part harmony using genetic algorithms. In: Di Chio, C., et al. (eds.) EvoApplications 2011. LNCS, vol. 6625, pp. 273–282. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20520-0_28 8. Arutyunov, V., A., Averkinb, A.: Genetic algorithms for music variation on genom platform. In: 9th International Conference on Theory and Application of Soft Computing, Computing with Words and Perception ICSCCW 2017, pp. 317–324, Budapest (2017) 9. Wiggins, G., Papadopoulos, G., Phon-amnuaisuk, S., Tuson, A.: Evolutionary methods for musical composition. In: Proceedings of the Second International Conference (CASYS 1998), pp.1–14, Liege (1998) 10. Marques, M., Oliveira, V., Vieira, S., Rosa, A.: Music composition using genetic evolutionary algorithms. In: Proceedings of the 2000 Congress on Evolutionary Computation, vol. 1, pp. 714–719 (2000) 11 There is also a hybrid unit (labeled as “ab” in the figure) that has a single descendent in segment

2.

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11. Moroni, A., Manzolli, J., Von Zuben F., Gudwin, R.: VoxPopuli: An interactive. evolutionary system for algorithmic music composition. Leonardo Music J. 10, 49–54 (2000) 12. Almada, C.: A transformational approach for musical variation. Orfeu 5(3), 373–411 (2020) 13. Almada, C.: Variation and developing variation under a transformational perspective. Musica Theorica 4(1), 30–61 (2019) 14. Almada, C. Derivative analysis and serial music: the theme of Schoenberg’s orchestral variations Op.31. Permusi 33, 1–24 (2016) 15. Almada, C.: Genetic algorithms based on the principles of grundgestalt and developing variation. In: Collins, T. et al. MMC 2015. LNAI, vol. 9110, pp. 42–51, Springer, Cham (2017) 16. Morris, R.: Composition with Pitch-Classes: A Theory of Compositional Design, 1st edn. Yale University Press, New Haven (1987) 17. Mayr, D., Almada, C.: Geometrical and vector representation of metrical relations. In: Proceedings of the Second Congresso da Associação Nacional de Teoria e Análise Musical (TEMA 2017), 10–19, Florianópolis (2017) 18. Dawkins, R.: The Blind Watchmaker, 4th edn. Penguin Books, London (2000) 19. Schoenberg, A.: Style and Idea: Selected Writings of Arnold Schoenberg, 3rd edn. Faber & Faber, London (1984) 20. Schoenberg, A.: Fundamentals of Musical Composition, 1st edn. Faber & Faber, London (1967) 21. Frisch, W.: Brahms and the Principle of Developing Variation, 1st edn. University of California Press, Los Angeles (1984) 22. Carpenter, P.: Grundgestalt as Tonal Function. Music Theory Spectrum 5, 15–38 (1983) 23. Haimo, E.: Developing variation and Schoenberg’s serial music. Music Analysis 16(3), 349– 365 (1997) 24. Simms, B.: The Atonal Music of Arnold Schoenberg (1908–1923), 1st edn. Oxford University Press, Oxford (2000) 25. Boss, J.: Schoenberg’s Twelve-Tone Music: Symmetry and the Musical Idea, 1st edn. Cambridge University Press, Boston (2014)

To the Question of the Possibility of Identifying the Psychophysiological Signs of “Ethnic Hearing” as Differential Perception of “Native” and “Alien” Music Alla V. Toropova(B)

and Irina N. Simakova

Moscow State Pedagogical University, Moscow 119991, Russia

Abstract. The paper is devoted to the overview of studies and the summary of methodological approaches to psycho-physiological features of listening, selective hearing, and perception of music. The scientific substantiation of such applied studies is aimed at the development of functional music and music therapy techniques. It is shown that psycho-physiological signs of perception of “native” and “alien” music by listeners of various cultures have been insufficiently studied. The main research goal of this review is related to the fact that a productive method of determining the way music influences individuals with different psychological and ethnic cultural characteristics has not been yet identified. In fact, the influence of the ethnic cultural factor in hearing music has not been considered as such. There are still no viable methods for defining the phenomenon of «ethnic hearing» in psychophysiological terms and no way to identify the psychophysiological peculiarities of hearing «native» and «alien» music. This study was conducted to investigate the psychophysiological signs of the response to listening to music; the influence on the psychophysiological signs by socio-cultural, personal, psychometric and neurohumoral factors; and whether the psychophysiological signs that indicate if listening to music is pleasant or unpleasant to the listener are identical to the psychophysiological signs of the musical perception influenced by the musical style and the ethnic-cultural experience of listening to music. The collected data for the review provides a methodological basis for the study of the phenomenon of “ethno-hearing” in the context of musical-psychological anthropology. Keywords: Listening · Ethnic hearing · Psycho-physiological features and observed indexes · Musical-psychological anthropology

1 Introduction Studying ethnic aspects of music listening is at the intersection of the related scientific fields of psychology of music perception, comparative music studies and ethnic musicology, which determines a wide range of related issues and a hybrid method that works for musicology, psychology and anthropology (Agawu 2003; Merriam 1969; Myers 1992; Nettl 1983, 2005). Studying ethnic aspects of music listening is more often understood © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. D. Khannanov and R. Ruditsa (Eds.): WWMC 2021, CRSM 9, pp. 68–81, 2021. https://doi.org/10.1007/978-3-030-85886-5_6

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as research in the music of other cultures («non-Western cultures»). Ethnic musicology includes the views on Western music from an anthropological or sociological standpoint. Comparative music studies have predominantly considered the music of oral folk traditions in comparison to the Western classical or contemporary written music tradition that has abandoned its oral origins and transformed the language structures and techniques of listening to music (Bartok 1931). Discussing the methodology of ethnic musicology studies, Bruno Nettl (1983) hypothesized that it is the product of Western thought, derived from subjective observations and assessments of «non-Western» music (Nettl 1983). There are objective restrictions to understanding and studying an «alien» culture because of the impossibility of avoiding the subjectivism in psychological or musicological considerations of the specifics of hearing music in various cultures. Izaly I. Zemtsovsky, a prominent Russian ethnomusicologist, suggested the concept of «ethnic hearing» for describing the phenomenon of the presence of the observer in a comparative-musicological study (Zemtsovsky 2009; 2012). The issue of an objective fixation of ethnic music hearing remains quite actual, including the organization of listening to music in «native» and «alien» cultures and the role of subjective selective factors in the hearing of music (Toropova and Knyazeva 2013). These factors are associated with different aspects of listener’s integral personality, including personal and ethnic cultural personality characteristics. The research into the psychophysiological signs of hearing music has been based on the fact that background music is frequently used in everyday life while driving, performing monotonous and/or office work and studying (Crawford and Strapp 1994; Fox and Ebrey 1972; Furnham and Allas 1999; Hallam et al. 2002). Listening to music is a widespread psychotherapeutic technique (Matsota et al. 2013). In most studies, researchers have concluded that background music improves productivity (Fox and Ebrey 1972), enhances studying performance (Hallam et al. 2002), accelerates memorizing (Hirokawa 2004.), cheers up (Sousou 1997) and reduces psycho-emotional stress (Hirokawa and Ohira 2003). There are the opposite indications as well: listening to music interferes with concentration during working and studying (Furnham and Bradley 1997; Jäncke and Sandmann 2010; Oldham et al. 1995). Whether passive listening to music helps or hinders cognitive activity depends on the personal qualities (extraverts are more susceptible to music than introverts) (Crawford and Strapp 1994) and the mood of the listener and the musical style (e.g., music by Brahms and Haydn is heard as pleasant only by those in a good mood, whereas the music of Mozart is always perceived as pleasant (Hallam et al. 2002; Jausovec and Habe 2003). All this also depends on the neurohumoral condition (a low level of neuro-steroids promotes sensitivity in hearing music (Bazanova and Mernaya 2008). Hearing music depends on the experience of recognizing its semantic component (Marie et al. 2011; Patel, Iversen and Rosenberg 2006). A productive method of determining the specific type of music and the way in which it influences individuals with different psychological and ethnic cultural characteristics has not been identified so far. In particular, the influence of the ethnic cultural factor in hearing music has not been

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considered. A method for defining the phenomenon of «ethnic hearing» in psychophysiological terms to identify the psychophysiological peculiarities of hearing «native» and «alien» music remains unknown. This literary research was conducted with the goal to investigate the psychophysiological response to listening to music and the way the socio-cultural, personal, psychometric and neurohumoral factors influence the psychophysiological reactions. We also set a goal to investigate whether the psychophysiological reactions to music as pleasant or unpleasant are identical to the psychophysiological signs of the musical perception influenced by the ethnic-cultural experience.

2 Objective Differentiation of the Signs of Musical Perception: A List of Possibilities 2.1 The Psychophysiological Signs of Musical Sensitivity According to Yekaterina A. Golubeva, the EEG index of “music skills” while performing music and the consequent lability of the nervous system is based on the ability to acquire («impose») photo stimuli of high frequency (18, 20, 25, 30 Hz and higher), whereas the signs of music perception and simultaneous weakness of the nervous system are shown by the indices of response to “imposing” low frequencies (2–4-6 Hz) in response to photo-stimulation and the power of delta-waves in the rest (Golubeva 2007). The author suggests that imposing low-frequency rhythms might heighten the sensitivity to aural perception of music. These data agree with recently published findings by Nozaradan et al. (2011), in which the EEG index of activation of the neuronal processes in recognizing music rhythm and tempo has a stable potential with the frequency of the recognized rhythm (Nozaradan et al. 2011); i.e., the music appears to “impose” its core rhythm on the neuronal oscillations. Tatiana S. Knyazeva and Alexander N. Lebedev found that hearing music, regardless of the type of music, is associated with increased power in the EEG theta- and betaranges (Knyazeva and Lebedev 2000); increased power of beta waves during listening to upbeat tempo music was also found by colleagues. During simultaneous EEG and EMG recordings, an increase in gamma power, accompanied with an increase in muscle tone, was found in response to listening to upbeat tempo music (van Deursen et al. 2008). Listening to music by Beethoven raised the skull muscle tone and the power of EEG high frequency waves in healthy persons; however, it did not influence the EMG and EEG indices of people suffering from dementia and Alzheimer’s disease (van Deursen et al., 2008). This finding suggests that the EMG indices of muscle tone, which is controlled by the central nervous system, are sensitive to the indices of the capacity to hear and perceive music. Detailed research into cortical muscular interactions has shown that an increase in the EEG signal power on the skull surface in the frequency ranges of over 13 Hz and below 5 Hz is predetermined for the most part by muscular and not by neuronal elements (Goncharova et al. 2003; Halliday et al. 1998; McClelland et al. 2012; Shackman et al. 2009). Contemporary researches show that visual EEG inspection and statistical software frequently could not eliminate the noise pollution of the electroencephalographic

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signal with low-amplitude electromyographic (EMG) artefacts (Fitzgibbon et al. 2012; Halliday et al. 1998; Hashimoto et al. 2010). The dedicated survey of gamma oscillations conducted by Whitham et al. is convincing in the suggestion that the power of waves with the frequency of over 20 Hz is generally determined by the EMG origin (Whitham et al. 2007). The data from the researchers who claim that the activity of the beta and gamma ranges is a sign of music perception must be interpreted by taking into account the EMG contribution to the electrical signal. The coherence of the EEG and EMG signals is one of the methodological grounds for the EEG recording under control of the EMG (Bazanova and Vernon, 2013; Chakarov et al. 2009), and it focuses the attention of electroencephalographers on the alpha-EEG range, which is the least coherent with the EMG signal (Halliday et al. 1998). The changes in the EMG of the frontalis muscle under the influence of music requires more detailed consideration because Paaschier, Hlem-Hylkema and Orlebeke showed that the EMG of the frontalis muscle is associated with the psychoemotional stress level (Paaschier et al. 1984). 2.2 EMG and Temperature Indices of Music Perception Although listening to music is often used by psychotherapists and implies general muscle relaxation (Choi et al. 2008; Lee et al. 2012), the issue of the influence of music on the EMG indices of psycho-emotional stress has rarely been investigated, and the data are controversial. Occasional research has found that the relaxing action of music is confirmed by a decrease in the amplitude of the frontalis muscle EMG (Blumenstein et al. 1995). Simple biocontrol training aimed at EMG decrease simultaneously relives psycho-emotional stress without music (Canter 1975; Engel and Andersen 2000). Passive listening to music, unlike training with feedback, does not decrease the EMG (Schilling and Poppen 1983). Most studies show that the influence of music on the frontal EMG depends on numerous factors, including the following: the type of musical stimulation (active music increases the EMG, and relaxing music decreases the EMG (Island 2007); the «ordinarity» or «extraordinarity» of the rhythmic pattern of the music for the listener (the EMG decreases while listening to an ordinary rhythmic pattern and increases while listening to a complicated and extraordinary pattern) (Safranek et al. 1982); the experience of listening to music (in persons with long experience listening to music, there is less activation, as measured by the EMG indices of the frontalis muscle tone (Egermann et al. 2013). Identical findings were obtained for the temperature of the fingertips, which is another psychophysiological index of psycho-emotional stress (Lai et al. 2008; Lin et al. 2012; Newton 2009). The temperature of the fingers rises if the stimulating material is relaxing music selected by researchers (Lai et al. 2008) or music selected by the subjects (Lin et al. 2012). Similar to the EMG reaction to the music, there was an increase in the blood circulation in the finger phalanx (an increase in temperature) depending on the style and tempo of the music (Bernardi et al. 2006) and on the subject’s experience in listening to music (Myskja and Lindbaek 2000) No viscerogenic index of psycho-emotional stress (the frequency of cardiac contractions and breath, the frontalis muscle EMG or the phalanx temperature) changed in green macaques under the effect of music, regardless of the tempo or rhythm (Hinds et al. 2007). These data, as well as research findings in the

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hearing of music by persons with mental disorders, show that the viscerogenic indices change while listening to music only if the music is perceived by the human psyche, i.e., by a listener with a music conscience. The EMG and temperature, as psycho-physiological indices of music hearing, could not be fully informative because they are subject to the influence of such purely “human” factors as a higher nervous function, the thinking style, the level of psychomotor experience, temper and other factors. It indicates that the key indices of the response to listening to music could be found in an analysis of neuronal activation. 2.3 Neurobiological Indices of Music Perception Gordon R.L., Magne C.L. and Large E.W. (Gordon et al. 2011) hypothesize that the basis of the assumption that hearing music predominantly depends on neuronal activity includes the following aspects: first, cortical rhythms are included in the structure of recognizing acoustic signals (Nozaradan et al. 2011); second, the participation of electric brain waves in recognizing rhythmic elements is determined by their role in selective attention (Jones 2010; Stefanics et al. 2010); and, third, the influence of sound leads to the activation of cortical processes (Jäncke and Sandmann 2010). The mechanisms of this activation are unknown. No other electrical brain oscillation from 10–2 to 103 Hz has such functional importance in the process of attention (Niedermayer 1997), memory, emotions (Cacioppo 2004), motivation (Bazanova and Vernon 2013) and general activation (Barry et al. 2007) as does the alpha rhythm (Nunez et al. 2001). The EEG alpha-activity indices might serve as markers of the cognitive activity success and optimal functioning (Barry et al. 2007; Bazanova and Vernon 2013; Halnsmayr et al. 2005). The connection between the alpha waves of the brain and music perception and processing has been emphasized by numerous authors (Bazanova et al. 2003; Flohr et al. 2011). The results of these studies are rather controversial because most authors identify alpha-oscillation activity only by the value of their amplitude or power in a specific standard range, which is a possible source of controversy in the interpretation of the described phenomena. Without an analysis of the separately determined indices of the frequency, phase and reaction of alpha waves to eyes opening, it is impossible to determine the signs of whether the listener liked the music or whether it had a psychotherapeutic effect (Bazanova 2003). The quantitative characteristics of the wave process include the amplitude, the frequency and the phase of oscillations (Crawford and Strapp 1994). The individual frequency of alpha waves is associated with the efficiency of solving cognitive tasks (Hanslmayr et al. 2005) and the ability to learn (Bazanova and Vernon 2013), whereas the intensity of phasal transformations is associated with the ability to find extraordinary solutions to creative problems (Bazanova and Vernon 2013; Klimesh et al. 2007). One of the main functional features of alpha waves is the so-called Bergereffect or the ability of these waves to lower the amplitude when the eyes are opened or under the action of cognitive and/or psycho-emotional stimuli, which is called activation (Barry et al. 2007; Berger 1929). Schaefer et al. (2011) found that musical imagination is accompanied by activation (alpha suppression) while listening, and vice versa, it weakens activation and increases the power of alpha waves. These results show that the “inner” hearing of music is related

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to attention intensification and is accompanied by increased activation (the depth of the alpha-amplitude suppression), whereas passive listening to music is accompanied by weakened activation, i.e., lower involvement of the neuronal generators in processing musical information (Schaefer et al. 2011). Activation measured by the depth of the alpha-amplitude suppression in the low- and high-frequency alpha ranges is secured by different molecular cellular mechanisms (Tenke and Kayser 2012) and is associated with different psychophysiological processes (Klimesch 1999; Moretti et al. 2010). The functional significance of these different frequency ranges might differ. Based on the results of the earlier studies (Klimesch 1997; Muravleva et al. 2012) we suggest that changes of power in the individual low-frequency alpha-1 range would be connected with involuntary processes (Bazanova and Vernon 2013) and with voluntary excitation and suppression in the high-frequency alpha-2 range. The total width of the alpha range reflects the number of different-frequency generators participating in the reaction to the stimulus and is associated with non-verbal creativity (Bazanova and Vernon 2013). The value of the total width of the alpha range and its low and high frequency components in the perception of music is unclear. The duration of the Berger-effect, observed in the alpha-1 range, was the longest in the condition and is characterized by the highest level of progesterone (Muravleva et al. 2012). It does not correlate with such physiological indices of activation as the level of cortisol and the frequency of cardiac contractions (Bazanova and Vernon 2013). The duration of the Berger-effect in alpha-1 range apparently shows other processes in the brain and does not show activation. According to Golubeva, the stability of the reaction to eye opening demonstrates the suppression of insignificant processes of activation for the central data processing (Golubeva 2007) of the so-called “top-down” control, which is related to the effectiveness of cognitive activity (Klimesch et al. 2007). The mechanism of how the signs of EEG alpha-activity appear (the increase or decrease in frequency, the growth or suppression of amplitude, the range width, the depth and duration of the activation reaction, the synchronization or desynchronization of the oscillation phases) in response to listening to music with different subjective values for listeners is unknown. 2.4 Dependence of the Psychophysiological Features of Music Perception on Neurohumoral Conditions The identical stimulus of equal intensity might lead to opposite reactions of psychophysiological systems subject to the initial condition of the body (Niedermayr 1997; Ordoñana et al. 2012). Despite the established dependence of reactivity and phenotypic specifics of the central and vegetative nervous systems (Bazanova 2012), the influence of the neurohumoral condition on the reaction indices to listening to music has rarely been studied. The natural model of neurohumoral change is the female menstrual period (Kaplan et al. 1990). The cyclical change of the level of progesterone, which is the main brain neurosteroid, is one of the most significant natural endogenous factors that inhibit the activation reaction (see the review in Compagnone and Mellon 2000). Primary pilot research found that an increase in the amplitude of alpha waves, as a sign of a comfortable condition, occurs while listening to cantilena music only in the low-progesterone

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level phase, whereas during the high-progesterone level phase, this phenomenon is not observed (Bazanova and Mernaya 2008). 2.5 Dependence of the Psychophysiological Features of Music Perception on the Dominant Archetype Pattern The creation of a perceptive image while listening to music is determined by at least two factors including the peculiarities of the musical form and the psychophysiological features of the listener’s personality. The precedence of the two factors has not been settled; either music with definite expressive features «imposes» initial changes in listeners with various psychophysiological patterns or an individual listener reacts differently to a given fragment of music. The search for significant personal archetypical complexes continues in various aspects of personal psychology according to the theories of K.G. Jung (Austin 2009; Dreifuss 2001). A.V. Toropova found that the perception of music depends on archetypical features personalities. An archetype is understood here as a complex of psychological properties and psychophysiological patterns that determine in the dominant type of intonation (the intonation archetype) and the archetype’s hearing is the filtration of significant image signals while hearing music (Toropova 2011). The authors’ pilot study (Toropova and Simakova 2013) established EEG-signs of hearing music with subjects with different dominant personality archetypes. The effect of all of the selected classical musical fragments led to similar changes in the electroencephalograms of the subjects with various archetypical signs. Under the influence of the musical fragments with different temporhythmic features, all of the groups showed an increase in the power of high-frequency alpha rhythms (11–13 Hz) in the paleo-encephalon and intensification of the slow-wave activity in the sensory and motor cortex. These changes were reliably and better expressed in the test group with the “enfant” archetype than in the subjects with the archetypical signs of “the sage” and “hero.” The study findings of the perception of varied music demonstrated that the archetypical factor of personal peculiarities influences the formation of a perceptive image while hearing music more significantly than do differences in the features of a musical form (the musical stimulus factor does not change the EEG hearing signs). This fact confirms the theory that each person hears more of themselves in music as their projected “Self” or remains indifferent. 2.6 Dependence of Psychophysiological Features of the Perception of Music on the Dominant Sensor Modality Listener Modern studies of the sensor modalities are generally associated with the consideration of psychophysiological changes under the stimuli of the following modalities: visual (Romei et al. 2012), hearing (Hartmann et al. 2012) and somatosensory (Valentini et al. 2012). Authors use the method of induced potential in many papers devoted to sensory perception. Our studies of conscious and unconscious responses to various types of music in which the subjects were differentiated by their dominant sensory modality of image representations when listening to music showed that subjects had various electroencephalogram features. In the group in which the dominant modality was visual, in quiet

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conditions, 100% of the subjects had an EEG with a high alpha rhythm index. If the dominant modality were kinesthetic, the EEG with a high alpha activity index was observed less often (in 44% of the patients). A one-way ANOVA test identified the minimum values of the power of beta rhythm and the maximum increase of the power of theta activity in the cortex central motor regions in the subjects, in which the dominant modality was kinesthetic while they listened to music. The subjects in whom the dominant modality was emotional demonstrated an increase in the beta activity index while listening to music (Toropova et al. 2011). 2.7 Dependence of Psychophysiological Features of the Perception of Music on the Given Compositional and Ethnic Musical Style A sufficient volume of data shows that music by different composers influences the psychophysiological indices of hearing music in different ways by the so-called «Mozart effect» (Perlovsky et al. 2013; Rausher et al. 1993). Mikutta et al. (2012, 2013) demonstrate that listening to the exposition of the first part of Symphony № 5 by Ludwig van Beethoven (in C minor, op. 67; duration: ~ 7.4 min) provokes suppression of the amplitude in the low-frequency alpha-range, which shows unconscious activation, whereas the response to music by Chopin shows a cardiac rhythm variability increase, which reflects a higher ability for conscious self-control (Mikutta et al. 2012; Mikutta et al. 2013). Based on this finding, the authors concluded that, depending on the composer’s inspiration, music might be an unconscious stimulus to activation or a stimulus entailing top-down control (Mikutta et al. 2012, 2013). Other authors showed an increase in power in the 9.6–11.4 Hz range while subjects listen to relaxing as well as active music, whereas the interhemispheric coherence rose only while listening to active music (Iwaki et al. 1997). Music with different characteristics by the same composer provokes different psychophysiological reactions, which is natural in terms of common sense and is the basis of adequacy in listening to music. Bazanova (2003) showed that an increase in the alphawave power in the low-frequency range might indicate a sentimental positive reaction to the cantilena section of the P. I. Tchaikovsky concerto for violin and orchestra (in D major, op. 35) and that an increase in power in the high-frequency range occurs while perceiving the third (active dancing) segment of the same violin concerto (Bazanova 2003). Thus, the perception of various music examples is accompanied by changes in different EEG alpha-activity features. 2.8 Dependence of Psychophysiological Features of the Perception of Music on the Experience of Music Perception and Socio-cultural Factors The integral human personality includes internalized language structures from a native culture. Conducting studies on the psychophysiological peculiarities of subjects from different ethnic cultural and musical language traditions while listening to music proved to be relevant. A psychological division of language structures into «external» and «internal» was made by N. Chomsky (Chomsky 1956, 1957). C. Lévi-Strauss hypothesized that music

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acts via two networks. The first is physiological, i.e., natural. The other is cultural (culture, in this context, is viewed as an external storage of sensor models, signs and symbols) (Lévi-Strauss 1964). The recent overview by James Rhys Edwards develops the theory of musical hearing “Between Inside and Outside”: (Edwards 2012). According to ethnic musicologist Izaly I. Zemtsovsky, this phenomenon is expressed by the concept of «ethnic hearing» (Zemtsovsky 2009, 2012). According to the limited published data, a definition of the phenomenon of «ethnic hearing», which is used in this paper as a key term, is not present in psychophysiological studies. It is used in other fields of knowledge and is often associated with the ease of recognizing related language structures (Peretz et al. 2004). The fact that there is the only publication (Hove et al. 2010) devoted to the comparison of absolute pitch among subjects of different nationalities suggests the need to study the neuronal correlates of listening to music while taking into consideration the ethnic and cultural factors of the subjects. Currently, there is no data on the interrelationship between EEG indices and the perception of «native» and «alien» music.

3 Conclusions Further research into data formalization and analysis and their multi-aspect correlation and interpretation in respect to «native» or «alien» intonation and language environment might solve the psychophysiological issue, «the cost of learning», of the contribution of brain flexibility in cognitive processes on the basis of «accepting» information in learning and broad informational space. In addition to objective signs of differences in the perception of “native” and “alien” music, the researchers use the methods of subjective psycho-semantics, which in the profile of assessments of a particular music show the differences in the dimension of the factor space, the power of the contribution of factors and their content (Toropova and Knyazeva 2017). There are no observable differences in the perception of classical music by professional musicians with different ethno-cultural origins. We can explain this by the influence of professional music education, its unifying effect in the treatment of music as classical art form. Nevertheless, the question remains unresolved and scarcely discussed: whether the studied classical music remains “alien” for its recipients who study it with a different ethno-hearing at the level of psychophysiological and/or neuronal reaction of an unconscious “cultural code”. Continuing research in a comprehensive methodology can help understanding the structure of musical experience, which combines the “archetypal codes” transmitted by national culture and traditions with the picture of the world perception obtained during training in a universal or foreign language cultured environment. Acknowledgement. This paper has been supported by the grant of Russian Foundation for Basic Research (RFBR) to the research project № 19–013-00171.

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The Musical-Theoretical Concept of Tatiana Sergeyevna Bershadskaya Daniil Shutko(B) Saint Petersburg Rimsky-Korsakov State Conservatory, ul. Glinki, 2, St. Petersburg 190000, Russia

Abstract. The article is devoted to the aspects of the musical-theoretical teaching of Bershadskaya, an outstanding Russian theorist and researcher. The author raises the questions of universality of musical theory and of the relationship between creative and scientific approaches. Various sound-pitch systems are considered, their systematization is presented in the form in which it has been offered by Bershadskaya. The author also addresses the issue of difficulty of adapting Russian terminology into English music scholarship. Keywords: Music theory · Harmony · Monody · Functions · Musical language

1 Introduction. About the Works of Bershadskaya Tatiana S. Bershadskaya (1921–2021) was a Soviet and Russian musicologist, professor at the Rimsky-Korsakov St. Petersburg Conservatory, head of the St. Petersburg school of harmony. Her main works include the early monograph Fundamental Compositional Rules in Multi-Voiced Russian Folk-Peasant Songs (1961) [7], Lectures on Harmony (first edition—1978) [4], a monograph Harmony as an Element of a Musical System (1997) [3], a very important terminological dictionary The Sound-Pitch Musical System (2013, with Elena Titova) [11], a large list of scientific and methodological works in various scientific collections and journals republished in author collections, such as Selected Papers of Different Years in two volumes [8, 9]. Throughout her long professional career, she created and constantly improved the musical-theoretical concept, in which the experience of the entire previous history of musical theory is generalized and systematized, including the works of her teachers, Yuri N. Tyulin and Khristophor S. Kushnarev. On the one hand, we can say that this concept is quite conservative in the good sense of the word, since it is associated with the entire history of thought about music, starting from the ancient times. But on the other hand, a clear, systemic, and unbiased view of the most diverse musical styles makes Bershadskaya’s ideas very fresh and avant-garde. Even today, one cannot say with confidence that her ideas are sufficiently understood by her colleagues. Bershadskaya was an unsurpassed polemicist. Her texts are distinguished by clarity and logical correctness of wording. The scientific rigor of her concept is combined with musical flexibility. Its main analytical goal is not to impose new additional meanings on the musical text, but © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. D. Khannanov and R. Ruditsa (Eds.): WWMC 2021, CRSM 9, pp. 82–92, 2021. https://doi.org/10.1007/978-3-030-85886-5_7

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to try, as deeply and authentically as possible, to reflect the processes that form these texts, their inner logic and musical essence. In this paper, I do not intend to consider all aspects of Bershadskaya’s concept (this task would exceed the limits of this genre), but I will try to draw attention to some important components of Bershadskaya’s concept that make it special.

2 General Approaches 2.1 Science and Creativity There are two fundamentally different, even opposite approaches to musical theory. One is strictly scientific, taking into account the achievements of previous theorists, aiming to find or develop the most accurate definitions, covering the possible widest range of musical phenomena. The other is rather creative. It involves the invention of new theories. It does not necessarily reckon with the theories of the past. The power of the author’s creative thought is valued here more than objectivity, proving that with a creative object — musical art, you need to work with a creative instrument of the corresponding character. Without assessing which of the two approaches is correct and which is not, it should be noted that Bershadskaya’s concept is an example of the first, strictly scientific approach. Her system is an evolutionary stage in the general theory of music, which dates back to ancient times, through the treatises of the Middle Ages and the New Age, the works of Rameau, Riemann, Kurt, Erpf, Reti, Schoenberg and Russian theorists: Yavorsky, Asafiev, Mazel, Tyulin, Kushnarev, and many others. The main advantage of Bershadskaya’s theory is the austerity of systematization. It is important to note: we are not talking about superficial classifications, with arbitrariness in most of which she had to fight, but with the most contemporary concept of systematic approach that science has provided. At the same time, in Bershadskaya teaching system, creative tasks are occupying the first place. She is convinced that a theoretician means nothing in his or her profession if he does not compose at least to some extent. In the process of studying, Bershadskaya invented various forms of non-traditional written works (for example, [6]). This created a unique creative atmosphere in her class, which proved to be indispensable in analysis of music. 2.2 Methodology Like any other science, music theory needs a reliable methodology. Bershadskaya does not use any mathematical methods. The results obtained using this methodology are usually insensitive to the distinction between creatively successful and creatively mediocre music. Mathematics remains only in the periphery, as an auxiliary tool. Her concept is much more concerned with the psychology of art perception, general psychology, the foundations of human logical thinking. Also, Bershadskaya’s theory was influenced by linguistic theories, both structuralist and post-structuralist. Bershadskaya calls the musical text the object of her research. Its analysis is based on the difference between language and speech aspects. Several key musical-theoretical categories have their prototypes in linguistics, such as the grammatical system of the language [2].

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Also, Bershadskaya considers formal logic to be the most important methodological basis of the theory of music, which is much more suitable for use in the humanities than mathematics. Some of the best examples of clarity of theoretical thought are Tchaikovsky’s book on harmony and Yury Tyulin’s texts. The latter exerted a strong influence on the entire Russian musical-theoretical scholarship of the Soviet period. Both were lawyers by first education and studied formal logic professionally. It was later reflected in the entire system of their theoretical thinking. 2.3 The Universality of Musical Theory Bershadskaya has been teaching harmony at conservatoires at the highest level of Russian music educational system since the beginning of the 1970s. In order to become her student, one must have had had solid training in in “school harmony”. Bershadskaya’s course goes beyond classical harmony. It is devoted to musical pitch systems in the entirety of their history and geography—from old forms to modern music. Moreover, while she referred to the examples from the contemporary music at the time of writing a book (for example, the music of St. Petersburg composers Sergei Slonimsky, Boris Tishchenko, etc.), her system was already open to the music of the next period. Bershadskaya builds her theory on the basic psychological and cognitive abilities. He intention was to develop the most general, universal, essential definitions of musical categories. Without them music is impossible in principle, while the basic forms change with time, from one musical style to another.

3 The System of Musical Lad (L-System) 3.1 Harmonic Functions An example of systematic approach in Bershadskaya’s concept is the issue of development of the theory of harmonic functions, T, D and S. In the 1970s, there was a wide discussion in Russian music theory about the nature of harmonic functions. The traditional Riemannian interpretation linked functions to specific chords located on first, fourth, and fifth degrees. The inviolability of the connection between a function and a specific structure was refuted by musical practice itself. And besides, such connection was a logical mistake. This limitation of Riemannian theory was overcome already by Riemann’s student Hermann Erpf, who introduced the concept of central chord to explain the complex chords of 20th century music as tonic [12]. According to Erpf, the structure of chord does not determine its function, and any chord can turn out to be tonic, if the composer defines its context in this way—he stops movement on this chord (by the way, neo-Riemannians, as I can understand, do not see this important development of Riemannian theory). Thus, it is impossible to explain function by structure. It was necessary to explain the logic of the function, which was done in Mazel’s great work Problems of Classical Harmony [16], on which Bershadskaya relies in solving this issue. Tonic—any chords on which the music stops (according to Erpf). The dominant is an unstable function that gravitates towards the tonic, and, as Mazel emphasizes, gravitates in a directional way, that is, “really wants” to move into the tonic,

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and knows where this tonic is. That is, it does not matter for the system whether the tonic sounds or not, since the dominant already shows where the tonic is, and this is enough for the system (recall, for example, the first number from Schumann’s “Im wunderschönen Monat Mai,” from the Dichterliebe, where the composer, using S and D in F-sharp minor, never resolved them into the tonic of F-sharp minor. But, despite the absence of the tonic, the key of F-sharp minor as a system, and its tonic as the center of this system undoubtedly exists! Mazel explained the subdominant in the spirit of Hegelian philosophy as an unstable function that is the antithesis of the tonic. This third function is the most important acquisition of the classical music system, which made it very stable compared to any other. Based on this, Bershadskaya concludes that in the case of harmonic functions we are dealing with a special pitch system, the essence of which is not in chords, but in movement. Some elements of this system require movement, others stop it. 3.2 Non-harmonic Functions In parallel with classical harmony, Bershadskaya studies other styles associated with both folk music (Russian in particular) and professional ethnic traditions (Armenian monodic music, thanks to her professor Kushnarev), which does not know chords. And within the framework of monody, the system is essentially the same, which is also responsible for the movement, but the elements of this movement are not chords, but tones, individual sounds. Bershadskaya compares melodies in different systems: monodic and harmonic. For example, such (Fig. 1).

Fig. 1. Old Russian church chant znamenny rospev (Stepenna, 8 glas).

In this example, the melody controls the movement, the tones move into tones, the tones act as stable and unstable elements (Fig. 2).

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Fig. 2. L. van Beethoven. Piano sonata #14 (op. 27, #2).

In this case, the melody is also the main means of musical expression. But harmony is responsible for stable and unstable areas (which means movement). The melody here, as Bershadskaya says (following Mazel), is like a queen in modern Western monarchies. She reigns but does not rule. And finally, one more case:

Fig. 3. S. Rachmaninoff. Etude-tableau c-moll. Op. 39 #7.

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Here, the melody regains its control function, just like in a monodic system. The chords follow the melody, coloring the tones of the melody, but without their own move/stop functions. This is a new, third type of epy system. Thus, in all three cases (these examples are from Bershadskaya’s article “The Lost Magistral” [9, pp. 118–124]), we are talking about the same system, with an essentially common functionality, but with a different form of elements that implement this functionality (tone or chord). This is how Bershadskaya comes to a very clear, essential description of the system in music, which in Russian terminology is called lad. It is difficult to find an analogue in English. There were the attempts to translate the lad as mode, but now it has become obvious to many Russian experts that it is completely insufficient. This is a logical pitch system (l-system) that distinguishes sound elements (they can be different: tones, chords, and then probably timbres and, possibly, some other ones in the future) according to the degree and form of their moving or stopping role. Thanks to this distinction, a system of relations of sound elements appears, primarily hierarchical in one form or another (Bershadskaya even uses the word subordinate). Through this distinction, basic musical information is transmitted, since according to general information theory, for the implementation of a communicative act, the brain must distinguish and logically connect informative elements. All the same applies to modern music, we are talking only about the changed sound forms of informative units. According to this position, musical communication is impossible without lad (l-system), and therefore—music. 3.3 Typology of L-Systems The lad-theory is divided into 2 large parts. One part deals with its functions. In most musical styles, both historical and modern, there are two of them: stable and unstable. There are intermediate options—for example, a local stable, which is unstable in relation to the main one, but has its own subordinates (like, for example, the repercussa in the Gregorian chant, in relation to the finalis it is unstable, but has its own sounds surrounding it). And only the classical system has 3 functions, which makes it special. The second part of this theory studies the elements—carriers of move/stop information (the informative unit of l-system). If these are tones, such systems are called monodic. If these are chords, such systems are called harmonic. This classification has many interesting analytical implications. For example, analyzing Bach’s counterpoint music reveals an interesting method that Bach invented. He completely mastered the system of harmonic functions (T, D, S) and learned how to use them in the conditions of one voice — one melody (Fig. 4). There is only one voice, but behind it, harmonic (and that is, chord) functions are clearly manifested. Tonic—thanks to the fourth c-g in the first motive. Then the change of function to a next beat — from the fifth step to the sixth—this can only be a subdominant. Then again to a next beat, a move down from the second step to the fifth—tonic (in this context, the dominant is impossible, because the previous D — the tone could also be dominant, and the function changes due to the metric position). And then there is harmonic cadence. After that—a scale in C minor. Then modulation in g-minor and harmonic cadence (T-D-T in g-minor). Now, let us look at the upper voice. The theme immediately begins in g-minor, from S (F sharp is the key indicator). What do we

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Fig. 4. J. S. Bach. Das wohltemperierte Klavier I. Fuga c-moll.

see? As soon as the upper voice enters, C minor sounds both above and below, but at the bottom it is the tonic of C minor, and at the top it is the subdominant of gminor. We have a functional and more—tonal contradiction, which, as a result, gives rise to dissonance between F-natural and F-sharp. This is a very important invention of Bach—to use harmonic functions to separate one voice more clearly from another, to create a counterpoint of a completely new power than it was before Bach. Bach uses polyfunctionality all the time. So, it can easily distinguish a bad (student) fugue from a good one. In bad fugue voices coincide vertically in one harmony. It is very difficult to write such a high-quality counterpoint as in Bach. 3.4 Monodic-Harmonic L-System In addition to the two named types of systems—monodic and harmonic, Bershadskaya discovers a third type of system. In this system, chords are present, but they have no functional meaning (see Fig. 3). The informative unit in such systems is the single tone, and the chord plays the role of only paint, which makes it possible to separate one tone from another. This system was invented in St. Petersburg in the second half of the 19th century. For several years the composers of the Five have been discussing the development of Russian music and looking for inspiration in the Russian peasant song, in which the tone was the informative unit, but which existed in conditions of polyphony. This idea was put into the basis of his musical language by Mussorgsky. He often used regular chords, but they do not behave the way chords should behave in the classical system, tonics, dominants, etc. Because of this feature, his music seemed wild to his contemporaries. Later, Rimsky-Korsakov, who joined the clan of academic composers, edited the works of Mussorgsky in order to give them a more fine in his opinion, more

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classical look. Bershadskaya has an interesting article about this story — how RimskyKorsakov edited Mussorgsky [8, pp. 70–89]. It possible to cite one short example from the introduction to the opera Boris Godunov (Fig. 5).

Fig. 5. M. Mussorgsky. Opera “Boris Godunov”. Introduction. Klavier by M. Mussorgsky and Klavier by N. A. Rimsky-Korsakov.

Mussorgsky writes chromatisms in different directions, as if separating one tone from another, which gives each of them a separate weight. Rimsky-Korsakov’s hearing links chromatisms into a more simple and familiar line. Another remarkable example is the piece “Tuileries (Children’s Quarrel after Games)” from the Pictures at an Exhibition (Fig. 6).

Fig. 6. M. Mussorgsky. Pictures at an Exhibition. “Tuileries”.

We see the key signature of B-major in the score, we hear the tonic of B-major, but in fact the B-major in this piece is a “fake”: there are no B-major functions (D, S). If we listen to the voices separately, we will hear that the upper voice is a monody based on dis (not the D-sharp-minor! There are no chords, only single tones). The lower—monody based on gis. There is also a fis voice in the middle. The B-major chord turns out to be a disguise for this polymonodic structure (this example was given not by Bershadskaya,

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but by Evgeny Trembovelsky, the composer and musicologist from Voronezh. But this example is fully consistent with the theory of Bershadskaya). Usually, in systems where monodic principles interact with chords, the expression modal harmony is used. Bershadskaya does not like this term, because it covers quite a lot of phenomena that are different in nature, without specifying them and working as an “umbrella”. Harmony of the 17th century, harmony of Mussorgsky, harmony of Debussy, jazz harmony—if to call all this modal harmony, then the essence of these different systems is lost. For example, Bershadskaya has a special article devoted to the fact that opposing modal and tonal harmony is a logical mistake and misunderstanding [9, pp. 43–50].

4 Conclusion L-system is an important, but not the only aspect, which is studied in detail in the Bershadskaya concept. Let us briefly designate others. Another system in which harmony plays a significant role is the musical texture system [in Russ. myzykalna tkan], literally translated as musical fabric, or spaceconstructive system. It’s responsible for the primary coordination of sound elements in the categories of consistency and simultaneity. Following Tchaikovsky, Bershadskaya calls consequent relationships a melody, and simultaneous ones—harmony. Thus, a melody in this aspect is any horizontal connection of sounds, regardless of their expressiveness. In this system, all categories that relate to space in music work: not only vertical and horizontal, but also, for example, depth, diagonal (according to Boulez), relations between relief and background. Within the framework of the aspect of musical fabric, Bershadskaya considers the principles of its structure (ideal level, only 3 types) and an infinite number of ways of their individual implementation in the musical texture (material level). It is interesting that in conditions of polyphonic fabric, Bershadskaya always takes into account both factors: vertical (harmony) and horizontal (linear connections). One of the factors is leading, directing the movement. The other is coordinating. Thus, in the conditions of counterpoint music, lines act as the leading factor, and harmony (in the form of a system of interval relations) coordinates the interaction of these lines. And, conversely, in a fabric based on chords, melody lines play a coordinating role (the rules of voice leading, from which the study of school harmony begins). The chords theory is also part of this aspect. Another system that Bershadskaya considers is a thematic system, the main function of which is the representation of the material: its individualization, the ability to memorize and recognize it (the fundamental work of another famous Leningrad professor and colleague Bershadskaya, Ekaterina A. Ruch’evskaia, is devoted to the study of this issue [18]). Among other musical systems, we will point out the syntactic, rhythmic, compositional (functions of the musical form), etc. Bershadskaya sees an important task of musical theory in not mixing these systems, correctly distinguishing between levels and aspects. In conclusion, I would like to emphasize that the theoretical concept of Bershadskaya, despite the severity of its provisions, or perhaps thanks to them, is open to any form of

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musical expression. This theory tries to very carefully and accurately reveal the nature and meaning contained in the text itself. It is difficult to find its analogues, from point of view of consistency and universality. It easily adapts to any, including the latest phenomena in musical composition. And, of course, it has not lost its relevance, just as it will not lose it in the foreseeable future.

References 1. Asafiev, B.V.: Muzykal’naya forma kak process [Musical form as process]. 2nd edn., vol. 2. Muzyka, Leningrad (1971). (in Russian) 2. Bershadskaya, T.: Analogies and parallels in the structure of music and verbal languages. In: Eismont, P., Konstantinova, N. (eds.) LMAC 2015. CCIS, vol. 561, pp. 3–10. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-27498-0_1 3. Bershadskaya, T.S.: Garmoniya kak element muzykal’noj sistemy [Harmony as an element of a musical system]. UT, St. Petersburg (1997). (in Russian) 4. Bershadskaya, T.S.: Lekcii po garmonii [Lectures on harmony]. 3rd edn. Kompozitor, St. Petersburg (2003). (in Russian) 5. Bershadskaya, T.S.: Leningradskaya–peterburgskaya shkola teorii muzyki [The Leningrad-St. Petersburg school of music theory]. In: Degtiareva, N. I. (ed.) Sankt-Peterburgskaya konservatoriya v mirovom muzykal’nom prostranstve [St. Pe-tersburg conservatory in a world-wide musical context], pp. 9–15. Politekhnichesky Institut, St. Petersburg (2013). (in Russian) 6. Bershadskaya, T.S.: Netradicionnye formy pis’mennyh rabot po garmonii v konservatoriyah [Non-traditional forms of written harmony work in conservatories]. 2nd ed. Kompozitor, St. Petersburg (2001). (in Russian) 7. Bershadskaya, T.S.: Osnovnye kompozicionnye zakonomernosti mnogogolosiya russkoj narodnoj krest’yanskoj pesni [Fundamental compositional rules in multi-voiced Russian folk-peasant songs]. Muzgiz, Leningrad (1961).(in Russian) 8. Bershadskaya, T.S.: Stat’i raznykh let (Selected papers of different years). Soyuz khudozhnikov, St. Petersburg (2004). (in Russian) 9. Bershadskaya, T.S.: Stat’i raznykh let — 2 (Selected papers of different years — 2). Kompozitor, St. Petersburg (2019). (in Russian) 10. Bershadskaya, T.S.: V ladah s garmoniej, v garmonii s ladami: ocherki [In modes with harmony, in harmony with modes: Essays]. St. Petersburg Conservatory, St. Petersburg (2011). (in Russian) 11. Bershadskaya, T.S., Titova, E.V.: Zvukovysotnaia sistema muzyki. Slovar’ kliuchevykh terminov. [The Sound-Pitch Music System. Glossary of Key Terms]. 2nd ed. Kompozitor, St. Petersburg (2013). (in Russian) 12. Erpf, H.: Studien zur Harmonie- und Klangtechnik der neueren Musik. Leipzig (1927). 13. Ewell, P.: Music theory à la leningrad: an interview with Tatiana Bershadskaya. Contemp. Musicol. 4(2019), 121–164 (2019) 14. Kholopov, Y.: Garmoniya: teoreticheskij kurs [Harmony: a theoretical course]. Lan’, Moscow (2003).(in Russian) 15. Kushnarev, C.: Voprosy istorii i teorii armyanskoj monodicheskoj muzyki [Questions on the history and theory of Armenian monodic music]. Gosmuzizdat, Leningrad (1958).(in Russian) 16. Mazel, L.: Problemy klassicheskoi garmonii [Problems of Classical Harmony]. Muzyka, Moscow (1972).(in Russian) 17. Rimsky-Korsakov, N.A.: Uchebnik garmonii [Harmony textbook]. St. Petersburg (1885). (in Russian)

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18. Ruch’evskaia, E.A.: Funktsii muzykal’noi temy [Functions of Music Thema]. Muzyka, Leningrad (1977).(in Russian) 19. Shutko, D.: Tjulin, Kushnarev, Bershadskaya: leningrad school of music theory in a dialogue with Schenker’s and Lehrdal’s Ideas. In: Long, V., Rockwell, J. (eds.) Program and Abstracts Thirty-Eighth Annual Meeting of the Society for Music Theory October 29–November 1, 2015. St. Louis (2015) 20. Tiulin, Y.: Stroenie muzykal’noj rechi [The structure of musical speech]. Muzgiz, Leningrad (1969).(in Russian) 21. Tiulin, Y.: Uchenie o garmonii [Studies in harmony], 3rd edn. Muzyka, Moscow (1966).(in Russian)

Sociology

About the Apollonian and the Dionysian: Dialogues Between Music and Wine in the Spanish Social Context Diego Pérez-Fuertes(B) , Emma Juaneda-Ayensa, and Cristina Olarte-Pascual Universidad de La Rioja, 26006 Logroño, Spain [email protected]

Abstract. In this paper, the precedents in the investigation of so-called soundscape in the perception of wine are explained first. They are related to the needs of the current market. Next, the design of an experiment on the subject through a survey is enunciated, which leads to the desire to learn more about the connections between drinking wine and the sound and social environment. Apart from this objective, the authors considered it appropriate to ask about changes in the habit of wine consumption during the pandemic, as well as to study the population that engages in such activity. The results regarding the first question are oriented in a causal direction, i.e., on the basis of data, there does seem to be a certain relationship between some musical genres and drinking a specific type of wine. These results diverge slightly depending on the scenario where consumption occurs. Changes in consumption derived from the pandemic are also reported, aimed at reducing it, with home drinkers having grown in numbers. It is concluded that the favorite combination is rock music and red wine for the general set of scenarios, and a sociological tendency is guessed in the Spanish population to carry out this consumption in large meals and late at night. (*) Keywords: Wine · Music · Soundscape · Pairing · Priming effect · Cross-modal correspondences

1 Introduction Knowing the intertwining relationship between music, wine, and its consumption scenarios and what contextual, cultural, and psychological norms it seems to obey, can be a key differentiator in today’s market. Even more so if we consider that a large part of this consumption is linked to very specific scenarios, i.e., contexts of relationship and exchange where drinking plays a fundamental role as a social modulator (Agnoli et al. 2011). Considering all the said above, it is necessary to investigate one of the most significant components in this interaction framework: ambient music, and by extension, the entire soundscape that participates in creation of such contexts. This work has been carried out in a situation of health crisis, in which wine consumption has decreased due to the disappearance of a large part of the social contexts traditionally associated with its consumption. This situation has caused a general decline © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. D. Khannanov and R. Ruditsa (Eds.): WWMC 2021, CRSM 9, pp. 95–106, 2021. https://doi.org/10.1007/978-3-030-85886-5_8

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during 2020 in both consumption (Spain: −6.8%; World: −2.8%; var int. 2019–2020) as in international trade (OIV 2020). The literature that allows us to illustrate the relationship between music and wine consumption scenarios is diverse. In this way, we can find in the consumer’s choice important links with factors not necessarily related to taste or economics (Hsu and Chen 2019). On the contrary, some authors point out that certain gastronomic decisions could be conditioned by ambient music based on acoustic (Biswas et al. 2018) or geographical (Zellner et al. 2017) criteria. This factor of choice can be clearly confirmed in the research of North et al. (1997) on French and German wines, where it is explained that there is an increase in sales from one country or another depending on the origin of the in-store music. We also have a similar experience in the conclusions by Areni and Kim (1993), which point out that customers spend more on wine if classical music is played in the purchasing scenario compared to top-forty, not in quantity but in value. De Luca and Campo (2019) present us with a multisensory study in which the importance of the auditory factor and how it affects the organoleptic perception of various wines is emphasized. In this case, significant modifications are noticed in the tasting of a Chardonnay (white), which is perceived as sweeter and more delicate in an ambient context of classical music, compared to the results of a Merlot, which is perceived as ‘less alcoholic’ when the tasting staff is exposed to loud pop music. In addition, Shih et al. (2009) suggests a strong correlation between some musical genres and certain types of wine (white, red), and how the type of music listened affects the taster’s taste perceptions. More specifically, changes in the perception of sweet and sour tastes have been reported when modifying the pitch of the background music in works by Crisinel and Spence (2010) and Crisinel et al. (2012). Another important example of the possible contextual association between music and wine consumption is found through the study of brain activity (Hsu and Chen 2019), through the analysis of associated waves. In this way, there is a significant difference in the register of the α, β and γ waves as a function of the associative degree between the musical genre (in the broadest sense of the word) and the wine consumed. The concept of “priming effect” is defined as a prior influence due to the context (environmental or sociocultural) (McNamara 2005) in circumstances of choice or judgment. This effect can be used as a modulating element to obtain a specific response in the study subject (Minton et al. 2017). The results for this specific case suggest that this relationship is strong, i.e., there is an influence of the musical genre used in the sound stimulus with a certain preference in tasting. To support what we have explained, we must turn to the psychological considerations on wine consumption that appear in Spence (2020) and in Wang and Spence (2015). In this article, the tendency to associate certain basic flavours with a specific soundscape is mentioned. To this must be added the references in the first article to an older one (Spence et al. 2013, [Spence 2020, p. 9]) where it is stated that: Tasting the wines while listening to matching music resulted in a small but significant increase in people’s rated enjoyment of the wine drinking experience as compared to tasting the same wines in silence.

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This statement seems to be supported by the results of North (2012), where a significant emotional link is explained between the background music and the scores given to the wine by the participants in a tasting scenario. If we focus on the use and influence of the soundscape on perceptions prior to tasting, more linked to the context itself, we can find in Spence (2012, p. 1) the following statement: Marketers can enhance their consumers’ product experiences by ensuring that the sound symbolism of the brand name, as well as any shape symbolism of/on the labeling, and even the very shape of the packaging itself, sets up the right (i.e., congruent) product-related sensory expectations in the mind of the consumer. Considering these prior findings on the role of music and consumption scenarios, selections of an appropriate pairing provide operators (promoters of music events, managers of restaurant businesses or creators of wine tourism experiences, among others), with opportunities to increase customer satisfaction. In order to further the knowledge about the stated aims of this paper, the following research questions are proposed: RQ1: What relationships do people establish between music genres and wine? RQ2: Are there significant links between music genres and wine consumption scenarios? RQ3: Has there been any significant change in consumption and social interactions due to the pandemic? RQ4: What is people’s favorite time to drink wine?

2 Methodology One of the most important factors when making meaningful comparisons between consumption scenarios and musical genres was finding precedents through which to establish the study categories for both. 2.1 Design and Choice of Categories Regarding the choice of scenarios, the use of nine consumption scenarios proposed in the Motivational Map of the Wine Consumer was initially considered, a study aimed at commercial purposes (Interprofesional del Vino de España 2019). Finally, it ended up betting on the four scenarios defined in Agnoli et al. (2011), which had originally been used to categorize the forms of consumption and choice of wine a priori compared to other drinks of generation Y in Italy based on contextual differences (restaurant, home, bar and nightclub). To choose the study music, the possibility of incorporating the sonic models used in Wang and Spence (2017) for the tasting experiences was considered first. After a negative assessment of the viability of proposing these same models, not in a tasting context but in a priori selection, as proposed in the present work, it was decided to select the study musical genres present in Peng-Li et. Al (2021), which limits experiences of a priori gastronomic choice and its results to four different genres: rock, jazz, classical and hip hop.

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2.2 How Was It Measured? This measurement was carried out through unconditioned selective processes, through the elaboration of a series of questions that directly concerned each of the three factors listed. In the case of the types of wine, the selection was based on reducing the possible choice to the range of so-called still wines. In this way, we reduced the possibilities to three classes: red, white and rosé. As already explained in the previous section, it was necessary to establish a prior link between these wines and how they would be associated with different musical typologies based on the subjective imagination. Therefore, the best option was to ask a question that would force the three different types of wines to be paired with the musical categories previously exposed: rock, jazz, classical and hip hop. In relation to the scenario-wine linkages, four fictitious social situations were constructed that responded to the potential wine consumption scenarios defined by the bibliography, accompanied by some pictures that stimulated the suggestion of the respondent in the illustration of the aforementioned scenarios. In order to create realistic consumer situations, the four scenarios were slightly transformed as follows: restaurant into informal, home into alone, bar into afterwork and nightclub into party. For each of them, one of the previously proposed wine options had to be chosen, or the nonexistence of it within the situation, i.e.: red, white, rosé or “no wine”. Finally, for each of the scenarios, a section for the selection of musical genres was also introduced, plus the absence of music, in the form: rock, jazz, classical, hip hop or “no music”. Likewise, for each of the genres mentioned, a musical piece was chosen that would serve as an example for the respondents. The main reason was that these genres are very plural in their artistic manifestations, and the mere mention can generate very different imaginaries in each listener. By introducing examples, we made sure that all the people participating in the survey had at least the same sound reference for each of the genres. Regarding the selection of the pieces, copyright-free music had to be selected to avoid problems with the distribution of the survey. In this way, various pieces were found according to this profile on Soundcloud and YouTube. Another of the premises that the music had to fulfill was not to be too “disruptive” contextually speaking. This fact would have pushed respondents to reject it in many consumer scenarios for this reason alone. Jazz: For this genre, a piece was selected that contained the classical instrumentation of jazz quartets: a horn (trumpet), piano, double bass and drums. https://soundcloud.com/rossbugden/upbeat-jazz-music-new-york-1924-copyrightand-royalty-free#t=0:53. Rock: This genre was one of the most problematic when it came to making a choice. It was necessary to find a song suitable for the four types of scenarios, strong enough to be able to illustrate festive contexts but slow to adapt to less energetic scenarios. Mainly, we wanted to avoid very loud elements, so we opted for a piece with a predominance of bass sounds. https://soundcloud.com/tunetankcom/oldways-a-night-in-texas-no-copyrightmusic#t=0:33.

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Classical: The first movement of Mozart’s Serenade No. 13 for strings in G major K. 525 was chosen because of its popularity. Although the degree of potential disruption is not exactly low for a trained ear, many people traditionally confer stability and ‘relax’ attributes to this work, despite the fact that the style presents many changes in dynamics. https://youtu.be/0RWnhckfPfo?t=116. Hip hop: At first, it was proposed to use lo-fi hip hop music as a representative model for this genre. It was later dismissed, as it could lead to too relaxing scenes in the collective imagination. In the end, the neutrality in the sound perception of the dynamics was chosen (neither too flat nor too abrupt), and a piece with funky influences was chosen. https://soundcloud.com/tunetankcom/musical-bakery-in-da-hood-vlog-hip-hopfunk-copyright-free-music#t=0:54. By analysing the results obtained, it was possible to study the connections between scenario-wine, scenario-music and, ultimately, wine-music, adequately addressing the possible biases derived from the forced correlation. This last step had to be considered, above all, taking into great consideration the possible deviations caused by the associative imaginary embodied in the first question. Table 1. Characteristics of the sample. Sociological factors Gender

– Women: 54.8% – Men: 45.2%

Level of education completed

– Basic: 4.6% – Intermediate: 26.3% – University: 69.1%

Wine consumption habits Wine consumer?

– Yes: 77.9% – No: 22.1%

Frequency of wine consumption

– – – – –

Never: 15.7% Less than one drink a week: 31.8% At least one drink a week: 15.7% 2–3 drinks a week: 15.7% More than 3 drinks a week: 21.2%

– – – –

Rock: 69.5% Classical: 58.5% Jazz: 33.2% Hip hop: 11.1%

Musical habits Musical genders usually listened (Over the total population)

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2.3 Application of the Model, Preparation of the Survey and Fieldwork The total sample was N = 217, corresponding to a Spanish population with special incidence in the provinces of La Rioja and Barcelona, born between 1935 and 2002. Sociological data are shown in Table 1. The survey lasted for a total of 10 days (05/09/2021–19/05/2021) and it was shared by various social networks for distribution: WhatsApp, Facebook, Instagram and Twitter.

3 Results 3.1 Musical Profile of the Respondents The population studied was asked about the type of music they usually listen to and, based on the results obtained, different musical profiles were identified, depending on the musical diversity to which they were accustomed: 1. 2. 3. 4.

Plurals: people who listen to three or more types of music. Duals: people who mostly listen to two types of music. Pure listeners: people who usually listen to only one type of music. Non-musicals: people who don’t listen to music.

As we can see in Fig. 1, in our sample we mostly found a pure profile, who only listened to a single type of music, followed by a group that combined two musical styles. Only 6% of the sample did not listen to any type of music of those proposed. Within the pure listeners, we find a predominance of rock music listeners, followed by classical music listeners, and a negligible percentage of people who exclusively listen to jazz and hip hop.

Fig. 1. Percentage of listeners according to variety and musical genre.

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3.2 What Does Wine Sound like? As reported in Sect. 2.3, the entire population studied was questioned about the possible relationships between the proposed musical genres and the three types of still wines, in order to check if there was any type of a priori association between both categories attributable to an extrinsic imaginary towards the consumption scenario. From the frequencies, the corresponding incidence percentages between the musical genre and the wine classes were calculated. These results are shown in Fig. 2. As we can see, there is a clear associative trend when it comes to pairing rock music with the consumption of red wine, corresponding to 63.1% compared to very residual choices of white and rosé wines. In the case of white wine, there is a certain tendency to associate it with classical music, followed by jazz, although the consumption of red wine is still important in both. Overall wine consumption associated with hip hop music is low for all three types of wine. 69.6% of the population states that they do not find any previous relationship between this genre and wine, although there is a predominance of rosé wine over the other two. However, the music for which the latter gets a significant consumption score is jazz music.

Jazz

34.1

Classical Hip hop

20.3

43.3 5.1

14.7

9.2

10.6

Rock 3.22.3 0.0

28.1 35.0

31.3

40.0 White

12.4

69.6 63.1

20.0

17.5

Rosé

60.0 Red

80.0

100.0

No wine

Fig. 2. Percentages of choice of wine a priori for each musical genre.

3.3 Music-Wine vs. Scenarios The response frequency was obtained for each of the resulting combinations between types of wine and musical genres (20 in total). These frequencies were considered for each of the transformed consumption scenarios (afterwork, alone, informal, party), after which the incidence percentages of each response in relation to the total were calculated. The results for each of the combinations are shown in Table 2. As can be seen, there is a series of combinations that stand out from the rest. These can be weighted independently of the scenario or, on the contrary, in specific relation to it. Thus, Fig. 3 shows a distribution in plots of the combinations for the first case (independent) and Fig. 4 represents the ten most successful combinations in relation to the scenario in which they occur.

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No wine, Classical No wine, Hip hop No wine, Jazz No wine, No music No wine, Rock Red, Classical Red, Hip hop Red, Jazz Red, No music Red, Rock Rosé, Classical Rosé, Hip hop Rosé, Jazz Rosé, No music Rosé, Rock White, Classical White, Hip hop White, Jazz White, No music White, Rock

Afterwork 0,2% 0,7% 0,9% 1,8% 3,1% 0,8% 0,3% 1,8% 1,3% 5,5% 0,1% 0,2% 0,1% 0,0% 0,7% 0,6% 0,8% 1,4% 0,9% 3,6%

Alone 3,0% 0,1% 1,4% 1,2% 0,5% 4,5% 0,3% 1,4% 0,5% 1,7% 1,5% 0,1% 0,7% 0,1% 0,3% 4,6% 0,1% 1,6% 0,7% 0,7%

Informal 0,3% 0,6% 1,0% 0,6% 0,3% 1,4% 0,5% 6,0% 3,2% 3,3% 0,0% 0,0% 0,5% 0,1% 0,2% 0,9% 0,6% 3,2% 1,4% 0,8%

Party 0,2% 2,9% 0,6% 0,6% 10,4% 0,0% 0,8% 0,3% 0,1% 5,0% 0,0% 0,2% 0,0% 0,0% 0,5% 0,0% 1,2% 0,2% 0,0% 2,1%

Total 3,8% 4,3% 3,9% 4,1% 14,3% 6,7% 2,0% 9,6% 5,1% 15,6% 1,6% 0,6% 1,3% 0,2% 1,7% 6,1% 2,6% 6,5% 3,0% 7,1%

We can affirm that there is a clear predominance of rock music, on the one hand, and the consumption of red wine on the other, for all scenarios. Apart from this, it is important to highlight a prominent incidence of non-consumption, especially in festive contexts associated with nightclubs.

Fig. 3. Distribution in plots of the combinations regardless of the scenarios.

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Fig. 4. Percentages of the ten most successful combinations classified according to the scenario in which they occur.

3.4 Wine in the Time of Covid To the open question “Have you noticed any change in your consumption habits since the beginning of the pandemic?”, 41.9% of the population studied answered “Yes” and 56.7% answered no. The remainder was made up of non-defining answers. Of the entire population that answered “Yes” to the question, 23.1% referred to an increase in consumption in these circumstances, while 37.4% reported a decrease in it. One of the most recurrent responses to the question was related to the context of consumption. With respect to all those who answered affirmatively to possible changes, up to 15.4% stated that they had started to drink more at home than outside compared to the previous situation. 3.5 Favorite Moments A treatment was carried out on the responses received to the question “What is your favorite time to drink wine?”, and a dichotomous matrix was constructed depending on whether they referred to day time, feeding time or both. Once the frequencies were obtained for both the time categories (midday, afternoon/evening, evening/night) and the meal type (snack, dinner/lunch, supper), the percentages for each secondary category were calculated in relation to their primary category. The results appear in Table 2.

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As we can see, there is a reasonable preeminence in the consumption of wine in the main meals compared to its use in the accompaniment of appetizers. Apart from this, we appreciate a tendency to drink wine at night, followed by events that take place at noon. The least common scene is the one corresponding to the afternoon (Table 3). Table 3. Moments of preference of wine consumption Moment categories Results in each category Day time

– Midday: 40.9% – Afternoon/Evening: 27.3% – Evening/Night: 57.6%

Feeding time

– Appetizer: 19.5% – Dinner/Lunch: 63.4% – Supper: 61.0%

4 Conclusions This research brought in the following results. In the first place, there seems to be a very clear association between red wine and rock music, both in the a priori and a posteriori data of the introduction of the scenarios, in addition to being a very appreciated tandem among those surveyed. To understand this trend, apart from a correlation that seems quite strong, it is necessary to introduce two possible influencing factors. The first is that, according to the data obtained in Sect. 3.1, a large part of the population studied is a habitual consumer of rock music, which could act as an independent conditioner from both the wine and the scenario. The second is the sample context, since in Spain a famous cocktail of red wine and cola called “kalimotxo” is quite popular. This drink is common in rock festival environments and, by association, could be linked to the “red wine” category. Another consideration about music-wine-stage relationships is silence. A small percentage of the people surveyed have expressed the wish that there be no music in everyday recreational scenarios (afterwork, informal). Although this percentage is not comparable to the rest of the population, it is by no means a fact that should be ignored. To satisfy the demands of this population sector, it would probably be enough to keep the ambient music at a moderate or low volume in the spaces where the aforementioned activities take place. Apart from all the above, we must comment on the effects that the pandemic has caused in the population studied. Although there is a certain percentage of people who have seen their consumption increase, the general trend has been towards a decrease in it. To this it must be added that a part of the population that previously consumed in specific hospitality establishments has started to exercise this consumption at home (*). It has been proven that there is a clear preference for drinking wine at large meals and in night-time situations, probably due to cultural factors typical of the Iberian context. In

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the months after the pandemic, a series of reunions will take place, and most of them will be celebrated by consuming outdoors. In the establishments where these celebrations take place there will be background music, and the choice of one place or another to consume could be conditioned, in part, by the soundscape generated, as we have been able to glimpse in this study.

5 Further Investigations One of the most important limitations when preparing the study has been the small number of musical genres, as well as the specificity of consumption scenarios. This has been the case because, although we can intuit a great variety in both categories in our daily lives, we have had to limit them due to bibliographic requirements, since the literature that fixes the genres and scenarios in such a specific field of research (music and wine) is scarce. In the future, it would be interesting to incorporate more types of music and new consumption scenarios. In relation to the aforementioned, it would also be necessary to significantly expand the sample. The statistical tools that allow us to extract information from the data require that the number of people be high in order to establish quality correlations. This is even more true if we increase the number of musical and contextual categories. Therefore, it would be desirable to be able to replicate this same study on a much larger population.

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Correction to: Proceedings of the Worldwide Music Conference 2021 Ildar D. Khannanov and Roman Ruditsa

Correction to: I. D. Khannanov and R. Ruditsa (Eds.): Proceedings of the Worldwide Music Conference 2021, CRSM 9, https://doi.org/10.1007/978-3-030-85886-5 The original version of the book was inadvertently published with an incorrect volume number, which has now been changed to 9. The book has been updated with the change.

The updated version of the book can be found at https://doi.org/10.1007/978-3-030-85886-5 © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. D. Khannanov and R. Ruditsa (Eds.): WWMC 2021, CRSM 9, p. C1, 2021. https://doi.org/10.1007/978-3-030-85886-5_9

Author Index

A Almada, Carlos, 57 J Juaneda-Ayensa, Emma, 95 M Meelberg, Vincent, 29 O Olarte-Pascual, Cristina, 95 P Pérez-Fuertes, Diego, 95

R Rawbone, Trevor, 41 Richter, Celina, 18 Ruditsa, Roman, 3 S Schmidt, Stefan E., 18 Shutko, Daniil, 82 Simakova, Irina N., 68 T Toropova, Alla V., 68

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. D. Khannanov and R. Ruditsa (Eds.): WWMC 2021, CRSM 9, p. 107, 2021. https://doi.org/10.1007/978-3-030-85886-5