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The lecture “Music, Mathematics and Computer Science” is subdivided into two parts. The fi rst part, “Music, Mathematics and Computer Science: History of Interaction” (see ICONI journal, No. 3, 2020) examines the processes of interconnection and interpenetration of various fi elds of music, mathematics and computer science, spanning the period from Ancient Times to the turn of the 20th and 21st centuries. The second part of the lecture: “Music, Mathematics and Computer Science: Particular Features of Functioning of Computer-Musical Technologies” is devoted to examining various aspects of developing and applying computer-musical technologies in contemporary musical practice, including musical composition, performance and the sphere of music education

Computer music technologies present an autonomous section in the domain of contemporary informational technologies, a complex of programs and apparatuses which makes it possible to carry out operations with sounds, to create and edit musical material, to form and perfect the process of musical education. The development of the methodology of mastery of this new category of musical instruments, as well as its developing international scholarly significance pose the problem of elaboration and utilization of a single terminological apparatus which could categorize the present phenomenon most precisely and fully. The article offered by the authors aims at revealing the possibilities of generalization of terminological elaborations existing in of various scholarly and pedagogical schools and traditions. Keywords: methodology of scholarship, computer music technologies, scholarly methodology.

En la segunda mitad del siglo XX, gran número de investigadores en el campo de la música demostraron un interés constante en categorías musicales como el espacio y el tiempo, cuya naturaleza fundamental y potencial unificador (integrador) son obvios. Sin embargo, a pesar de la indudable contribución a la consolidación de las conclusiones, era necesario seguir mejorando los estudios sobre música, tanto en lo que respecta al contenido como al aparato de investigación lógico (incluidas las matemáticas). En el artículo se examinan estos aspectos del modelo integral del espacio semántico de la música en la teoría y la práctica de la investigación moderna y su repercusión en el sistema de educación musical contemporánea.

The article reveals the psychological aspects of the perception of music and interaction with it when using music computer technologies, which are a software and hardware complex (musical computer, keyboard synthesizer, DJ console, smartphone with sound programs, etc.) in conjunction with the methodology of its application in creativity and in music training. Revealing the contradictions that are typical for the educational field “Art: Music”, the authors propose and use in their research an interdisciplinary approach (psychology, neurophysiology, pedagogy, computer science and Information & Communication Technology) in a holistic consideration of the phenomenon of music in connection with the phenomenon and processes of its perception, creation, and translation. The main problem is identified as the need to identify and take into account the psychophysiological factors that affect a person when interacting with music. The goal is to study the effect of convergence of the music computer technologies, manifested through the phenomenon of polymodality of perception of an artistic image is solved through the analysis of existing interpretations of polymodality, related connotations and classifications of synesthesia, using examples of technological and cultural manifestations of the polymodal nature of perception (syncretism of arts, associativity as a method of interpretation of an artistic image). Discussed insights on the future prospects of the study of polymodality of perception and representation of the artistic image of a musical work as one of the key features actualized in music computer technologies the effect of convergence and to explore the effect of virtualization, the use of potential of these technologies and multimodal nature of human perception for the holistic understanding of works of art.

Currently, when planning research, we can use the most active research approaches, such as experiment and modeling. Taking as an example a model of a musical fragment based on the statistics of notes, this article presents a sample of an interdisciplinary study. The idea of the study is to develop several equations that can quantify some of the verbal characteristics of a musical fragment. To prove the relevance of these equations, we found out the relationship between the parameters of the integral model and the values assigned by experts characterizing the psychological impression from music of a certain musical fragment. We used the group of 70 students as experts who evaluate the music fragments for several verbal values. Then we used several formulas on the model parameters (probability matrix determinants). Taking each pair of expert and calculated values we try to find the correlation. If the correlation is high for some pair of calculated data and expert data, we can use this equation to estimate the verbal characteristic of a musical fragment. As the result of this study we have proven formulas (on the music fragment probability matrix) that can evaluate some verbal characteristics of any music fragment. The development of musical computer technologies (MCTs) and digital musical instruments allows for appropriate experiments, also related to the field of music education. The results of modeling the process of musical creativity using MCTs are of particular importance for the implementation of various types of inclusive music education.

The issues considered in the article actualize the problems associated with the characteristic features of teaching and educating students in the context of online educational the process using e-learning systems that are typical for teaching humanities. The authors identify the most appropriate approaches to the formation of educational programs in this area using distance learning technologies. The authors of the article rely on the characteristic educational elements of the Moodle distance learning system, which allows organizing the training of students as future teachers, taking into account the fact that their professional activity is associated with teaching various creative disciplines for children studying in preschool educational institutions and in the lower grades of secondary schools, lyceums, gymnasiums. The article is also devoted to the problems of teaching music informatics, which performs a limiting role and fills up the content components of education in the process of introducing distance learning forms into the pedagogical practice of music teachers.

The article deals with the regional folklore as a field of interaction of academic musical culture in the Far East of Russia and China. There is an analysis of both the aborigines’ culture and the Eastern Slavic immigrating culture of the Russian Far East as well as of the indigenous culture outside Russian borders in Asia and the Pacific. Some common features of the Russian Far East and Chinese folklore are found out. There is a description of the concept of “academic musical culture” which comprises a composer’s work, successively associated with the foundations of Western European music that were formed during the period of 17th - 19th centuries (including the 20th century composers’ work as well as contemporary composers’ techniques), musical performance, music and performance infrastructure, educational space and academic musicology. The article highlights fundamental research in the field of studying the traditional musical culture of the Far East and China, research in the field of musical culture of the region along with the use of musical computer technologies in various fields of musical art and education.

The lecture “Music, Mathematics and Computer Science” characterizes by concrete examples various aspects of interaction of these studies with each other by incorporating the apparatus of corresponding scholarly disciplines (set theory, probability theory, information science, group theory, etc.). The role and meaning of these aspects in the formation of an integral perception about music and in the realization of practical creative musical goals are educed. Examination of these questions is what the lecture studies are devoted to as part of the educational courses “Mathematical Methods of Research in Musicology” and “Informational Technologies in Music” developed by the authors for the students of the St. Petersburg Rimsky-Korsakov State Conservatory and the Herzen State Pedagogical University of Russia. The lecture “Music, Mathematics and Computer Science” is subdivided into two parts. The fi rst part, “Music, Mathematics and Computer Science: History of Interaction” examines the processes of interconnection and interpenetration of various fi elds of music, mathematics and computer science, spanning the period from Ancient Times to the turn of the 20th and the 21st centuries. The second part of the lecture: “Music, Mathematics and Computer Science: Particular Features of Functioning of Computer-Musical Technologies” (due to be published in the journal’s next issue) is devoted to examining various aspects of developing and applying computer-musical technologies in contemporary musical practice, including musical composition, performance and the sphere of music education.

The article analyzes the issues of gathering and arrangement of folk musical materials, examines contemporary informational resources and technologies as a means of preservation and transmission of musical folklore. The Far East is a unique ethnic region inhabited by bearers of various cultures on its region, however, traditional folk music is rapidly disappearing, as the bearers of these languages are gradually dying out. Musical computer technologies (MCT) may become a perspective tool for mastery, transmission and preservation of phenomena of musical culture, in connection with which there arises the necessity of the swiftest implementation of MCT into the practice of activities of folk music researchers. Disclosure of unique specimens of traditional musical creativity, the study and comprehension of the most valuable collected materials, and the work on deciphering – all of these have not lost their relevance. The authors emphasize the important role of further professional elaboration, cataloguing, classification, systematization and digitization of data. The article gives support to the idea of a “musical bank” and an “intonational catalogue” of examples of musical folklore. Accentuation is given to the issue of creation of an education-related space in the domain of the Internet with application of the opportunities for MCT, which demonstrate themselves, among other things, as a new means of accumulation and transmission of knowledge about music. The authors come to the conclusion about the ability of MCT to play a significant role in the process of mastery, transmission and preservation of the musical culture of the Russian Far East, as well as the development and popularization of the traditional cultural heritage of the multinational state of Russia. Keywords: musical computer technologies, traditional musical culture, musical culture of the Far East of Russia, intercultural communication, transmission of musical culture.

The article provides teaching materials on the use of mobile technologies in the music-theoretical courses of children’s art schools. The use of mobile technologies allows teachers to organize their teaching activities (create a portfolio or a website), create an environment for remote support for learners (virtual classroom with assignments, tests, etc.), change the principles of classwork and homework by means of mobile applications and by making training programs personal and individual, adapted to the needs of each student. Tablets and gadgets have always attracted children, therefore, these familiar devices and the element of game and competition (various music applications) can help music-theoretical courses become much more interesting, draw children’s attention and energize them.

espanolLos procesos de informatizacion transforman el entorno de actividad profesional de un profesor de musica contemporanea, provocan la formacion de nuevas necesidades educativas de estudiantes de especialidades musicales y pedagogicas, requieren cambios significativos en las actividades de un profesor de musica relacionadas con la creacion y el uso de la educacion digital. recursos, la introduccion generalizada de tecnicas y metodos de interaccion de red. La tecnologia informatica de musica (MCT) permite aplicar de manera efectiva la experiencia pedagogica de la ensenanza musical tradicional y las nuevas caracteristicas de una computadora musical moderna. EnglishThe processes of informatization transform the environment of professional activity of a contemporary music teacher, cause the formation of new educational needs of students of musical and pedagogical specialties, necessitate significant changes in the activities of a music teacher related to the creation and use of digital educational resources, the widespread introduction of techniques and methods of network interaction. Music computer technology (MCT) allows for applying effectively the pedagogical experience of traditional music teaching and the new features of a modern musical computer. portuguesOs processos de informatizacao transformam o ambiente de atividade profissional de um professor de musica contemporânea, provocam a formacao de novas necessidades educacionais de estudantes de especialidades musicais e pedagogicas, requerem mudancas significativas nas atividades de um professor de musica relacionadas a criacao e uso de instrumentos digitais educacionais. recursos, a introducao generalizada de tecnicas e metodos de interacao em rede. A tecnologia do computador musical (MCT) permite aplicar efetivamente a experiencia pedagogica do ensino tradicional de musica e os novos recursos de um computador musical moderno.

The various aspects of formation and development of the musical instrumentarium disclose the main regular occurrences of functioning of musical instruments as synthesizers of musical sound in all its diversity, from the sources of their formation to the contemporary stage of the present process. In the fi rst lecture, “The Architectonics of Musical Sound” there was detailed examination of the particularities of the structure, the diversity and the various interpretations of the concept of “musical sound,” as well as the connection with the contemporary technical possibilities of notation, preservation and elaboration of musical sounds. In the present lecture the author turns to the main stages of evolution of the concept of “musical sound,” which refl ects the changes of sound material itself during the course of development of musical practice. The emergence of new musical instruments or musical synthesizers, according to the authorial conception, is stipulated by two main reasons. The fi rst of them is musicians’ aspirations of enriching the palette of their musical artistry. The second reason is connected with the historical perfections of the musical instrumentarium, which in its construction aspires to rely on contemporary achievements of science and technique in the domain of creation of sound. The level of development of contemporary program and machinery means of musical computer technologies (MCT) makes it possible to model diverse stages of development of systems of musical sounds.

The article analyzes the processes of information, transforming the educational environment of children with profound visual impairment. It emphasizes the need for changes in the content of musical education in connection with the use of specialized software and hardware, digital educational resources. The features of the process of teaching music using musical computer technology for blind people, which is due, in particular, the complexity of the complex psychological reactions of people with profound disabilities

At the turn of the 20th and 21st centuries there appeared a new trend in musical composition and musical pedagogy conditioned by the fast development of electronic musical instruments: from the simplest synthesizers to powerful musical computers. In the wide range contemporary electronic musical instrument the accumulated informational technologies in music and the art of music making have manifested themselves in the fullest and most perfect manner. The current and the subsequent issues of the journal shall provide a consecutive presentation of four lectures, compiling the basis of the discipline “Informational Technologies in Music” and a set of programs of advanced training, which include “Informational Technologies in Music,” “Informational Technologies in Musical Education,” “Computer Musical Composition,” etc. The first lecture, “The Architectonics of Musical Sound” shall disclose themes connected with the study of the physical characteristics of musical sounds, the means of their recording and reproduction; explanation is given to the aural perception of sound by the human being, and the basic principles of computer generation of musical sound are examined. The material elucidated in the lection possesses a theoretical and practical directedness and contains information in which the technological aspects of contemporary perceptions of music, about the musical instrument range (including computer musical instruments); without knowledge of these aspects a competent interpretation of musical instruments is impossible.

The “Listening to Music” course is an important link in the music education of a child. The “Listening to Music” course fosters love and interest in music, teaches to understand its language, and develops emotional responsiveness in children. The article considers new opportunities in teaching the “Listening to Music” course, which appeared along with a music computer, and which is more often used in the children's music school and meets the requirements of modern pedagogy. The article describes the capabilities of music and computer programs aimed at developing creative abilities of children. The authors examined new forms of work in the classroom using a music computer. The article proves that using a musical computer opens up broad prospects for employing creative tasks at children's music and art schools. The “Listening to Music” course is an important link in the music education of a child. The “Listening to Music” course fosters love and interest in music, teaches to understand its language, and develops emotional responsiveness in children. The article considers new opportunities in teaching the “Listening to Music” course, which appeared along with a music computer, and which is more often used in the children's music school and meets the requirements of modern pedagogy. The article describes the capabilities of music and computer programs aimed at developing creative abilities of children. The authors examined new forms of work in the classroom using a music computer. The article proves that using a musical computer opens up broad prospects for employing creative tasks at children's music and art schools.

O estudo se torna relevante pela busca das abordagens mais apropriadas para o desenvolvimento pedagógico dos novos recursos da tecnologia da informação, aplicáveis ao ensino interativo de música - por exemplo, ensinar a tocar um instrumento musical com o uso de um programa de computador. O objetivo do estudo é considerar a interatividade, a interação em rede e a implementação de funções educacionais como principais recursos das tecnologias de computador da música (MCT). Essas tecnologias podem ajudar a desenvolver uma metodologia eficaz para treinamento apropriado e novos sistemas de software e hardware com os quais os alunos podem aprender três dos componentes mais importantes da habilidade musical: o teclado de um instrumento específico, notação musical e teoria musical. Os autores concluem que o MCT pode e deve atuar como um ambiente educacional de rede interativa, e é necessário preparar uma lista de repertórios para o processo educacional nessas condições, bem como buscar formas organizacionais legais dessa atividade., El estudio se hace relevante mediante la búsqueda de los enfoques más apropiados para el desarrollo pedagógico de las nuevas características de la tecnología de la información, aplicables a la enseñanza musical interactiva, por ejemplo, enseñar a tocar un instrumento musical con el uso de un programa informático. El objetivo del estudio es considerar la interactividad, la interacción de la red y la implementación de funciones educativas como características clave de las tecnologías informáticas de música (MCT). Estas tecnologías pueden ayudar a desarrollar una metodología efectiva para la capacitación adecuada y los nuevos sistemas de software y hardware con los cuales los estudiantes pueden aprender tres de los componentes más importantes de la habilidad musical: el teclado de un instrumento en particular, la notación musical y la teoría musical. Los autores concluyen que MCT puede y debe actuar como un entorno educativo interactivo en red, y es necesario preparar una lista de repertorio para el proceso educativo en tales condiciones, así como buscar formas organizativas legales de esta actividad., The study is made relevant by the search for the most appropriate approaches to the pedagogical development of information technology’s new features, applicable to interactive music teaching––for example, teaching to play a musical instrument with the use of a computer program. The aim of the study is to consider interactivity, network interaction, and the implementation of educational functions as key features of music computer technologies (MCT). These technologies can help develop an effective methodology for appropriate training and new soft- and hardware systems with which students can learn three of the most important components of musical skill: the keyboard of a particular instrument, musical notation, and musical theory. The authors conclude that MCT can and should act as an interactive networking educational environment, and it is necessary to prepare a repertoire list for the educational process in such conditions, as well as to search for legal organizational forms of this activity.

The authors analyze the possibilities of examining the logical regularities in music by means of mathematical methods which have been formed for the most part in the 20th century. The proposed integrative model for the semantic space of music originated as a generalization of some analogous theoretical results obtained earlier by other researchers. The methods discussed in the article including, in particular, the basic ideas of such fields of research as set theory, the theory of probabilities and the theory of information, as well as the principles of soft computing, make it possible to elicit the premises of these scholarly branches in more traditional manifestations of music theory. The considered theoretical ideas and generalizations are remarkable as a basis for the precise study of various components of the system of musical thinking, including its synaesthetic area. The last of these aspects is important in the modeling of synaesthesia as a special case of virtual reality by means of computer technology and, thus, the use of music as a source of such realities. In connection with the ideas of direct inclusion of the visual range in music by computer means, such modeling becomes important not only for the synthetic forms of artistic activity with the participation of music, but also for the art of music itself. The authors of the article also touch upon some aspects of application of mathematical approaches to music in the sphere of musical education. Keywords: mathematics and music, musical semantic space, music theory, musical education, music computer technologies.