Retrospective Review of the Development of the Concepts of Consonance and Dissonance: On the Problem of Musical and Aesthetic as well as Physical and Mathematical Interpretation

"The research aimed at a comprehensive retrospective analysis of the development of “consonance and dissonance” as a musical and aesthetic category in physical and mathematical interpretation; defining the notion of consonance as a musical theoretical and aesthetic category, confirming the relevance of its use in physical and mathematical terminology to explain acoustic phenomena. Research methodology is based on the use of the retrospective method (or the retrospection method), which allowed identifying the theories of consonance and dissonance in the historical retrospective. The periodization method was used to find out individual stages in the development of science in order to discover the leading directions of scientific thought, identify new elements relating to various aspects of “consonance” and “dissonance”. The study of the retrospective review of the development of the notions of consonance and dissonance in the physical and mathematical interpretation involved an interdisciplinary method a way of organizing research work, providing for the interaction of music and mathematics in the study of consonance and dissonance. Scientific novelty. This study is the first to reflect the general tendency towards the mathematization of the humanities and the humanitarization of the physical and mathematical areas of modern culture. Some provisions of musical acoustics were clarified in the context of creating a harmonious conceptual structure. The article presents the author’s concept of clarifying the notion of phase in relation to the spectral structure of an audio signal based on the notion “slightly mistuned consonance”. Conclusions. A retrospective review of the development of the notions of consonance and dissonance in the physical and mathematical interpretation was carried out and presented as a comprehensive description and review of the formation of concepts in the temporal sequence of their creation. Retrospectiveness through a review of significant discoveries and achievements in music and natural science allowed tracing the formation of the theories of consonance and dissonance from the standpoint of the interdisciplinarity of modern knowledge in the humanities. The further process of the development of sound musical art technologies requires a significantly higher scientific level of their study, the creation of a coherent conceptual system based on modern physical and mathematical sciences as well as computer science to explain sound acoustic phenomena. Keywords: consonance, dissonance, mistuned consonance, overtone, harmonics, beats, phase, spectral component"

The Use of Mathematical Statistics Methods in Modelling the Psychophysiological «Value» of Cognitive Activity of Students with Different Levels of Academic Success

Mathematical interpretation of the psychophysiological «value» of modern schoolchildren’ cognitive activity will allow to identify risk groups, especially among students with high and average academic achievement. The results allowed to establish dependence of the type of functions and properties, at the expense of which the «value» of the students’ activity was manifested, from the way of organizing the educational process. The article argues that regression models of psychophysiological «value» have different filling of variables depending on gender, intensity of information and physical loads. The variables that are most often included in psychophysiological «value» regression models, i.e., are the most important markers of change in the «price» of activity of students with high academic achievement, include thinking flexibility level, extraversion, anxiety level, speed of complex visualmotor reaction, as well as average length of cardiocycles during mental activity.

Mathematical Interpretation of Global Competition between Payment Systems

The present study seeks to present a mathematical interpretation of the perception of new entrants to the global payments market on whether FinTech’s innovations promote competitiveness in the market. The study also quantitatively evaluates the competitive trends observed in the global payments market. The sampling frame consists of 504 respondents across 28 countries. The study is based on the analysis of the survey results using SPSS Statistics and Stata. The survey addressed four groups of factors influencing the competitiveness of the payment system (i.e., ‘Costs’, ‘Service Channels’, ‘Privacy and Security’, ‘Quality and Efficiency’). The respondents believe that FinTech innovations have a strong positive effect on the payment system’s competitiveness (M = 4.32). The results of the present study may be of interest to specialists and researchers who deal with the competitive dynamics of the global payments business, with payment innovations, and with convergence and transformation of the payments industry.

To the Issue of Mathematical Modeling of the Red Mud Thickening Process

The article focuses on the main mathematical modeling principles for engineering processes. The physical model of the red mud thickening process has been formed. The choice of mathematical model type has been described where the mathematical model represents the physicochemical character of the thickening process and allows estimating pulp water-yielding features at the stage of compression. Mathematical modeling of the engineering process, based on the studies of physicochemical patterns in its course and consideration of these patterns in the mathematical model, does not have certain disadvantages. Experimental data, used at the mathematical model formation where the mathematical model represents the physicochemical mechanism of the process, serve for their further analysis, physicochemical and mathematical interpretation. The mathematical model should be used as a method for detecting internal patterns in the process and for identification and quantitative assessment of its features.

A Survey on Contactless Gesture based Interactions

Gesture Based Interaction is the mathematical interpretation of human motion by a computing device. Contactless Gesture Based Interaction with devices aims to offer new possibilities to interact with machines thereby enabling development and design of far more natural and intuitive interactions with computing machines. The system makes use of static and dynamic gestures in order to perform operations on a system. This paper provides a detailed review on contactless systems which facilitates a better means of interaction between humans and machines.

A Mathematical Interpretation of the International Classification of Headache Disorders 3rd Edition

International Classification of Headache Disorders (ICHD3) provides definition of headache disorders that can be used to construct a mathematical basis for headache classification. We seek to construct a theoretical framework for such a construction.Headache and facial pain conditions are interpreted as bundles of phenotypes. ICHD3 diagnoses are then defined as sets. We proceed to show that observations, in the form of theorems, can be proved with our set theoretic construction for the ICHD3.The all-present “not accounted for by another ICHD3 diagnosis” criterion must be removed in order for our system to be set theoretic consistent. Furthermore, our system can be used to construct a categorical approach to headache medicine in the tradition of category theory.Mathematical interpretation of ICHD3 is possible and may provide significant implication for understanding the structure and organization of headache diagnostic classification.

Homeostasis Equation: An Approach to Theoretical Medicine

Homeostasis is kind of force that makes living organism to live. In this study, we suggest an integral equation that models homeostasis in living organism. We also showed that various situations can be modeled by homeostasis, and give mathematical interpretation of mechanism of living organism. With our proposed integral equation, one can handle homeostasis quantitatively, and this approach is expected to unveil various hidden properties of living organism.

Analisis interpretasi matematis dalam mini riset mahasiswa melalui pembelajaran berbasis riset

Statistics are studied in many fields of study including in Governmental Science, University of Muhammadiyah Malang (UMM). However, in reality, many UMM Government Science students do not understand the material and still have difficulty applying statistical methods, so it is necessary to provide mini research-based learning and analysis of interpretation abilities. The purpose of this research was to analyze students’ interpretative abilities in mini-research on research-based learning. The research used a qualitative descriptive method. The research sample consisted of 1 student who carried out mini research-based learning. The results of student’s reports were analyzed according to the indicators of interpretation ability. The result of the research indicated that the application of research-based learning in statistics subjects has a positive impact on students’ mathematical interpretation abilities can be seen from the achievement of the mathematical representation indicators found in the mini-research conducted by subject 1 in class. However, several things need to be improved in the mini-research conducted by subject 1, namely presenting problems and solving them in other forms. The descriptor wrote the notation in other forms and communicates the notation according to the idea.