Systematic Mathematical thinking reflected in the Semiology of the Musical Language

Author(s):  
Ioan OARCEA ◽  
Author(s):  
Dmytro Malyi

Background, objectives and methodology of the research. The social and cultural paradigm of the 20th century has given rise to a type of composing thinking that did not exist before – a scientific one. Thus, the evolution of the composer’s writing can be defined as a path from thinking by perfect consonance, emancipated dissonance to thinking by deterministic sound and its parameters (height, duration, dynamics, timbre, and articulation). The term of the «composer’s writing technique» means a set of techniques and methods of working with the musical material as a result of the activity of thinking/awareness. Therefore, the aim of this article is an attempt to explore the relationship between the compositional process and writing techniques of the 20th – 21st centuries (pointillism, aleatorysonorous, algorithmic composition), as well as the specifics of polyphonic, homophonic writing in a new context. The methodology of the study includes references to the scientific works by P. Boulez (1971), K. Stockhausen (1963), V. Medushevsky (1984), M. Bonfeld (2006), I. Beckman (2010), I. Kuznetsov (2011), K. Maidenberg-Todorova (2013), M. Vysotska and G. Grigoryeva (2014). Presentation of research results. The phenomenon of writing techniques is very important in the study of the specifics of the compositional process, as it is the technique, for the most part, becomes the goal of creation for many composers of the 20th century. In addition to new techniques, polyphonic and homophonic writing have undergone some changes. The polyphonic one has specific features that are manifested in linearity, part-writing, etc. Examples can be found in the works by D. Ligeti (micro-polyphony), R. Shchedrin, V. Bibik, V. Ptushkin, V. Sylvestrov, and O. Shchetynsky. Regarding the homophonic writing, we shall note that, first of all, it is an indicator of style and conceptual thinking of a composer (works by A. Pyart, J. Tavener, and L. Sumera). In pointillism, the sound is thought of as a deterministic, isolated structure, which is expressed by its various parameters. Here are the examples from the creative work by A. Webern («The Variations for the Piano»; «The Variations for the Orchestra»), by E. Denysov «DSCH». The aleatory-sonorous technique is associated with the operation of timbre sonorities, according to their specific patterns, and developed in the 50–60s of the 20th century in the works by I. Xenakis, V. Lyutoslavsky, Ksh. Penderetsky, and D. Ligeti. The algorithmic composition is an indicator of scientific and mathematical thinking, and is divided into: fractal, stochastic, spectral, concrete and electroacoustic music. The first was formed within the framework of the works by C. Dodge, G. li Nelson, D. Ligeti, and others (I. Beckman, 2010). Stochastic music is associated with the name of I. Xenakis, and the ancestors of the spectral school are the French composers G. Grisey and T. Murray. Conclusions. The article considers the writing techniques of the 20th–21st centuries as components of the compositional process. It can be concluded that the studied techniques are fundamentally interconnected, revealing the nature of the composer’s thinking/consciousness from different positions. The presented techniques are: the objectification of sound forms, the method of creation; the fact of the composer’s consciousness; the consequence of the historical and cultural evolution of the musical language and communication.


1996 ◽  
Vol 41 (1) ◽  
pp. 80-80
Author(s):  
Daniel Stalder ◽  
Shubhangi Stalder

PsycCRITIQUES ◽  
2010 ◽  
Vol 55 (23) ◽  
Author(s):  
Gordon Pitz

Author(s):  
Naomi A. Weiss

The Music of Tragedy offers a new approach to the study of classical Greek theater by examining the use of musical language, imagery, and performance in the late work of Euripides. Drawing on the ancient conception of mousikē, in which words, song, dance, and instrumental accompaniment were closely linked, Naomi Weiss emphasizes the interplay of performance and imagination—the connection between the chorus’s own live singing and dancing in the theater and the images of music-making that frequently appear in their songs. Through detailed readings of four plays, she argues that the mousikē referred to and imagined in these plays is central to the progression of the dramatic action and to ancient audiences’ experiences of tragedy itself. She situates Euripides’s experimentation with the dramaturgical effects of mousikē within a broader cultural context, and in doing so, she shows how he both continues the practices of his tragic predecessors and also departs from them, reinventing traditional lyric styles and motifs for the tragic stage.


1983 ◽  
Vol 2 (1) ◽  
pp. 81-93 ◽  
Author(s):  
V. Kofi Agawu
Keyword(s):  

Erich Wolfgang Korngold (1897–1957) was the last compositional prodigy to emerge from the Austro-German tradition of Mozart and Mendelssohn. He was lauded in his youth by everyone from Mahler to Puccini and his auspicious career in the early 1900s spanned chamber music, opera, and musical theater. Today, he is best known for his Hollywood film scores, composed between 1935 and 1947. From his prewar operas in Vienna to his pathbreaking contributions to American film, this book provides a substantial reassessment of Korngold's life and accomplishments. Korngold struggled to reconcile the musical language of his Viennese upbringing with American popular song and cinema, and was forced to adapt to a new life after wartime emigration to Hollywood. The book examines Korngold's operas and film scores, the critical reception of his music, and his place in the milieus of both the Old and New Worlds. It also features numerous historical documents—many previously unpublished and in first-ever English translations—including essays by the composer as well as memoirs by his wife, Luzi Korngold, and his father, the renowned music critic Julius Korngold.


2020 ◽  
Author(s):  
Jennifer McDonald ◽  
Rebecca Merkley ◽  
Jacqueline Mickle ◽  
Lisa Collimore ◽  
Daniel Ansari

Research in cognitive development has highlighted that early numeracy skills are associated with later math achievement, suggesting that these skills should be targeted in early math education. Here we tested whether tools used by researchers to assess mathematical thinking could be useful in the classroom. This paper describes a collaborative project between cognitive scientists and school board researchers/educators implementing numeracy screeners with kindergarten students over the course of three school years. The Give-A-Number task (Wynn, 1990) was used with first-year kindergarten students and the Numeracy Screener [BLINDED] with second-year kindergarten students. Results indicated that educators (N = 59) found the tools feasible to implement and helpful for exploring their students’ thinking and targeting instruction. The Educators’ feedback also helped inform improvements to the implementation of the tools and future directions for both the schools and the researchers. This work emphasizes the importance of transdisciplinary collaboration to address the research-practice gap.


2018 ◽  
Vol 13 (13) ◽  
pp. 100-113
Author(s):  
Y.V., Netsvitay T. V. Tararoev

Background. Goals In recent years, there is a growing interest in musical thinking, which is a key element of musicology and music philosophy, since music is a conscious, mental activity of a person and understanding the mechanisms of this activity, we can signifi cantly expand and deepen our understanding of music. The purpose of this study is to defi ne and supplement and clarify the concept of M. G. Aranovsky musical thinking our author’s approach, concretizing and clarifying the methodological and heuristic function of symmetry in musical thinking and its anthropological content. The work uses methods of comparison, analysis and synthesis. Musical thinking manifests itself in three forms of basic musical activity - composing, performing, listening, to which we also add theoretical (research) and pedagogical They are based on the processes of musical thinking and the fulfi llment of certain goals: the creation of an artifact, interpretation, reproduction, perception, analysis and theoretical understanding. The three spheres of realization of musical thinking are emotional-sensual, rational-logical and textual, semantic. These forms are closely intertwined and function on the basis of musical language, which is the foundation of any musical creative activity. The direct interaction of music and rationality is displayed in terms of “musical logic” and “architectonic musical ear”. Logic is the science of the most common laws of thought. These laws of thinking are expressed in the most abstract forms, patterns, rules that can be interpreted as conformity of something to specifi c norms, patterns. With regard to music, logic implies following certain standards and rules. Since the rational principle in music is closely associated with the irrational unconscious, the common logical norms that have been formed in a certain historical epoch within the framework of the dominant system of musical language are refracted through the individual stylistic features of the composer. A specifi c type of thinking - musical - generates the corresponding type of logic. Therefore, it is possible to express musical thinking by the sum of concepts - musical logic, musical speech and semantics of musical speech. M. G. Aranovsky identifi es four layers of musical logic: combinatorial, linguistic, contextual and artistic, i.e. those aspects (levels, edges) of the creative activity of a musician, in which there is logic. The lowest and at the same time fundamental level of musical logic is combinatorial, it is the sphere of primary elementary logical combinations of the simplest elements. However, the logic of this level extends to all scales of structures, from small motive links to sections of a one-part form. M. G. Aranovsky proposes to distinguish three types of logical combinations: 1. Identical - based on a constant repetition of structural units, where the formed elements are identical with each other (for example, AAAAAA). In terms of symmetry, this is a transformation of a simple movement along the time axis. It can again be noted as the simplest type of isomorphism, where only one characteristic changes - temporary. If we exclude it from consideration, then we can say that this is a “degenerate case” of isomorphism, which is an automorphism. 2. Equivalent - based on the modifi ed version of the repetition, in which there are both similarities and differences, i.e. incomplete identity is formed (for example, A1A2A3A4). From the point of view of symmetry, this combination of sequences represents the “unity” of the operation of symmetry, movement and violation of symmetry as such, i.e. in this sequence, some properties are repeated, while others change. This temporal process can be represented as isomorphism in the proper sense of the word, when some elements remain identical, while others change, and in general the objects are different, but similar. 3. Alternative - a combination of sequences of different units with complete exclusion of formal or obvious similarity (for example, ABC). Through symmetric transformations, this kind of logical combinations of primary elements can be described as an even greater symmetry violation, which preserves only the general “sequence of elements”, i.e. a small number of common properties, while these elements themselves are significantly different from each other. In this case, one can speak of a deep “transformation” of isomorphism, which can be called “metamorphism” (gr. Metamorphoómai - transformation of form). The basis of this transformation is a violation of the original symmetry in such a way that much more properties change than in the case of isomorphism. It can be schematically represented as A1 → B, A2 → C, etc. Thus, metamorphism can be considered both as a similarity, which has undergone a rather strong transformation, and as a symmetry violation, leading to a signifi cant complication of the structure. Thus, the result of this study is the position that, from the point of view of M. G. Aranowsky, the temporal process is the basis of musical thinking. The built-up chain “temporal process → musical logic → musical thinking” is the anthropological specifi city of human thought (in the musical sphere) associated with temporal processes in which a person is “immersed” and from which he cannot “exit” under any circumstances. Findings. we conclude that this chain can be called the “temporal-anthropological triad”. It represents the sequence “automorphism → isomorphism → metamorphism”. Each of its stages is different from the previous increase in the level of complexity. Of particular interest is the transition from isomorphism to metamorphism, since it is associated with the process of symmetry breaking. The mechanisms and principles of this disorder need further investigation.


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