MATHEMATICAL FOUNDATIONS OF MUSIC BY AL-FARABI

2020 ◽  
Vol 71 (3) ◽  
pp. 24-30
Author(s):  
N.T. Oshanova ◽  
Keyword(s):  
Music Theory ◽  
Arithmetic Operations ◽  
Scientific Idea ◽  
Mathematical Foundations

This article discusses the mathematical foundations of al - Farabi music, and suggests the main actions of arithmetic operations with Farabi relations to obtain musical intervals. Farabi drew attention to some problems for the study of musical art. This article provides an extensive understanding of how the three main problems are needed to get the ratio. Musical intervals have different values. You can divide them, multiply them, and listen to them. In music theory, you need to be familiar with the mathematical foundations for working with ratios, as well as arithmetic operations like multiplication, division, and addition. Farabi not only gives a scientific idea of the ratio of sounds, but also reveals the mathematical foundations of the emergence of harmony and musical melodies.

Perspective on Practice

2018 ◽  
Author(s):  
Jan Beran
Keyword(s):  
Computer Technology ◽  
Music Theory ◽  
Ancient Greece ◽  
Active Area ◽  
Musical Composition ◽  
Mathematical Ideas ◽  
Modern Computer ◽  
Mathematical Foundations ◽  
Modern Computer Technology

This chapter discusses the role of mathematical music theory in musical composition. Mathematical studies of music go far back in history. Some of the earliest documented come from the Pythagorean school in ancient Greece. Leibniz called music the ‘arithmetic of the soul’. The mathematical foundations of music have become an immensely active area of research in the last few decades. In conjunction with modern computer technology, mathematical tools are accessible to composers at an intuitive level. In this chapter, the usefulness of mathematical ideas for musical composition is illustrated by selected examples related to algebra and the theory of symmetries.

Conscious and Unconscious Reward Cues Can Affect a Critical Component of Executive Control

2011 ◽  
Vol 58 (5) ◽  
pp. 370-375 ◽  
Author(s):  
Rémi L. Capa ◽  
Gaëlle M. Bustin ◽  
Axel Cleeremans ◽  
Michel Hansenne
Keyword(s):  
Correct Response ◽  
Executive Control ◽  
Critical Component ◽  
Arithmetic Operations ◽  
Component Process

The present study investigates whether updating an important function of executive control can be driven by unconscious reward cues. Participants had to memorize several numbers and update those numbers independently according to a sequence of arithmetic operations. At the beginning of each trial, a reward (1 euro or 5 cents) was presented, either subliminally or supraliminally. Participants could earn the reward if they found the correct response on the updating task. Results showed better performance when a high (conscious or unconscious) reward was at stake compared to a low reward. This suggests that subliminal information can influence a component process of executive control traditionally thought to require consciousness.

Tasks of computer graphics under conditions of fundamentalization of preparation of an informatics teacher

2020 ◽  
pp. 57-63
Author(s):  
Ye. Yi. Bidaibekov ◽  
V. V. Grinshkun ◽  
S. N. Koneva
Keyword(s):  
Computer Graphics ◽  
Basic Principle ◽  
Fundamental Component ◽  
The Future ◽  
Scope Of Application ◽  
Education Training ◽  
Mathematical Foundations

The article deals with computer graphics tasks related to the activities of the future informatics teacher in conditions of fundamentalization of education. Training of future informatics teachers in the context of the fundamentalization of education requires them to know the range of tasks related to computer graphics and the skills to solve them. In order to enhance the fundamental component of computer graphics, methods are proposed that rely on interprandial communications, as well as on in-depth training of computer graphics. In the course of reasoning, the authors come to the conclusion that the content of computer graphics should be enriched with mathematical foundations of computer graphics and as a result update the content of the computer graphics course with machine graphics algorithms. The basic principle of selecting the content of the course offered is the principle of the fundamentalization of education. Since the scope of application of computer graphics is extensive, in our opinion, the system of tasks and tasks on computer graphics is the most interesting. A feature of this system is the orientation towards solving fundamental problems of computer graphics. It was also revealed during the study that it is possible to reduce the tasks of the proposed system to a certain sequence of stages. The application of stages for a certain type of tasks affects the methods of solving them. Thus, the fundamental training of future informatics teachers in computer graphics requires them to know these stages and methods of solving fundamental computer graphics tasks.

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