INNOVATIVE TECHNIQUE OF WORKING WITH MUSIC TEXT BY SYMMETRY OPERATIONS

Introduction: the article presents a new methodological approach to the study of the musical text using symmetry operations, which allows to achieve the highest level abstracted representations of musical works and bring it closer to mathematical modeling. This technique is particularly relevant whe...

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Autor principal:	Yuliya A. Brazhnikova
Formato:	article
Lenguaje:	RU
Publicado:	National Research Mordova State University 2016
Materias:	music and mathematics mathematical model in music symmetry in music music theory ear training melody variation transposition retrograde Education L
Acceso en línea:	https://doaj.org/article/9d36ac6a7f6c49a18cc8ac6821c52afc
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spelling	oai:doaj.org-article:9d36ac6a7f6c49a18cc8ac6821c52afc2021-12-02T00:30:50ZINNOVATIVE TECHNIQUE OF WORKING WITH MUSIC TEXT BY SYMMETRY OPERATIONS 10.15507/1991-9468.085.020.201604.507-5211991-94682308-1058https://doaj.org/article/9d36ac6a7f6c49a18cc8ac6821c52afc2016-12-01T00:00:00Zhttp://edumag.mrsu.ru/index.php/en/articles-en/63-16-4/495-10-15507-1991-9468-085-020-201604-07https://doaj.org/toc/1991-9468https://doaj.org/toc/2308-1058Introduction: the article presents a new methodological approach to the study of the musical text using symmetry operations, which allows to achieve the highest level abstracted representations of musical works and bring it closer to mathematical modeling. This technique is particularly relevant when teaching students without musical training and do not know the music reading. Materials and Methods: the work presents the technology of constructing a mathematical model of the musical text of any complexity on the basis of symmetry transformations. The research methodology is based on the practical consideration of the separate reception of sound and rhythmic sequences. Replacing the research object – a piece of music – a mathematical model has allowed to come to a very formalized notion of simple and complex musical processes and easily change their parameters during the simulation. Results: used formulas and symbols allow you to include music notation material in various information systems, reflecting in mathematical form the most important properties of a musical composition, or fragment thereof, as a system of symmetric relations. The study of these relations means of mathematics, in addition to the pedagogical value, should answer these questions about the properties of a certain set of pitch of a musical work relations. The article carried the description of the symmetry operations (broadcast, mirroring and translation-mirror transformation). The work involves two types of symmetric equality: classical symmetry and similarity symmetry. The first applies to zvukotsepochke (sequence of sounds separated from rhythm) and rhythm, which are located in real time. The second considers the harmonic sequence of sounds and ritmodoley is temporal factor. Discussion and Conclusions: in addition to the expansion of university disciplines “theory of music” and “ear training” in the specialty “Music education”, the use of categories of symmetry in music helps to significantly enrich the possibilities simmetrologii, which is now considered one of the fundamental branches of knowledge. In general, the use of balanced standards in music can become the basis for new directions in various areas of science and music used as an effective methodological tool, suggesting the possibility of its use in a multilevel process of working on the works of various styles. It should be noted that overseas the problem of musical symmetry is investigated with the 70-ies of the last century. In Russia and in the CIS countries, it began to be considered a little later and has not yet become widespread, despite the undeniable practical value. This issue can also be considered as part of informatization of education and better integration of music theory with the exact sciences.Yuliya A. BrazhnikovaNational Research Mordova State Universityarticlemusic and mathematicsmathematical model in musicsymmetry in musicmusic theoryear trainingmelodyvariationtranspositionretrogradeEducationLRUИнтеграция образования, Vol 20, Iss 4, Pp 507-521 (2016)
institution	DOAJ
collection	DOAJ
language	RU
topic	music and mathematics mathematical model in music symmetry in music music theory ear training melody variation transposition retrograde Education L
spellingShingle	music and mathematics mathematical model in music symmetry in music music theory ear training melody variation transposition retrograde Education L Yuliya A. Brazhnikova INNOVATIVE TECHNIQUE OF WORKING WITH MUSIC TEXT BY SYMMETRY OPERATIONS
description	Introduction: the article presents a new methodological approach to the study of the musical text using symmetry operations, which allows to achieve the highest level abstracted representations of musical works and bring it closer to mathematical modeling. This technique is particularly relevant when teaching students without musical training and do not know the music reading. Materials and Methods: the work presents the technology of constructing a mathematical model of the musical text of any complexity on the basis of symmetry transformations. The research methodology is based on the practical consideration of the separate reception of sound and rhythmic sequences. Replacing the research object – a piece of music – a mathematical model has allowed to come to a very formalized notion of simple and complex musical processes and easily change their parameters during the simulation. Results: used formulas and symbols allow you to include music notation material in various information systems, reflecting in mathematical form the most important properties of a musical composition, or fragment thereof, as a system of symmetric relations. The study of these relations means of mathematics, in addition to the pedagogical value, should answer these questions about the properties of a certain set of pitch of a musical work relations. The article carried the description of the symmetry operations (broadcast, mirroring and translation-mirror transformation). The work involves two types of symmetric equality: classical symmetry and similarity symmetry. The first applies to zvukotsepochke (sequence of sounds separated from rhythm) and rhythm, which are located in real time. The second considers the harmonic sequence of sounds and ritmodoley is temporal factor. Discussion and Conclusions: in addition to the expansion of university disciplines “theory of music” and “ear training” in the specialty “Music education”, the use of categories of symmetry in music helps to significantly enrich the possibilities simmetrologii, which is now considered one of the fundamental branches of knowledge. In general, the use of balanced standards in music can become the basis for new directions in various areas of science and music used as an effective methodological tool, suggesting the possibility of its use in a multilevel process of working on the works of various styles. It should be noted that overseas the problem of musical symmetry is investigated with the 70-ies of the last century. In Russia and in the CIS countries, it began to be considered a little later and has not yet become widespread, despite the undeniable practical value. This issue can also be considered as part of informatization of education and better integration of music theory with the exact sciences.
format	article
author	Yuliya A. Brazhnikova
author_facet	Yuliya A. Brazhnikova
author_sort	Yuliya A. Brazhnikova
title	INNOVATIVE TECHNIQUE OF WORKING WITH MUSIC TEXT BY SYMMETRY OPERATIONS
title_short	INNOVATIVE TECHNIQUE OF WORKING WITH MUSIC TEXT BY SYMMETRY OPERATIONS
title_full	INNOVATIVE TECHNIQUE OF WORKING WITH MUSIC TEXT BY SYMMETRY OPERATIONS
title_fullStr	INNOVATIVE TECHNIQUE OF WORKING WITH MUSIC TEXT BY SYMMETRY OPERATIONS
title_full_unstemmed	INNOVATIVE TECHNIQUE OF WORKING WITH MUSIC TEXT BY SYMMETRY OPERATIONS
title_sort	innovative technique of working with music text by symmetry operations
publisher	National Research Mordova State University
publishDate	2016
url	https://doaj.org/article/9d36ac6a7f6c49a18cc8ac6821c52afc
work_keys_str_mv	AT yuliyaabrazhnikova innovativetechniqueofworkingwithmusictextbysymmetryoperations
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INNOVATIVE TECHNIQUE OF WORKING WITH MUSIC TEXT BY SYMMETRY OPERATIONS

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