The Integrative Model for the Semantic Space of Music: Perspectives of Unifying Musicology and Musical Education
Main Article Content
Abstract
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.
Article Details
Copyright
The rights on the results of intellectual activity and equated means of individualization are protected in accordance with Part IV of the Civil Code of the Russian Federation. The authorship, author's name, executor’s name, inviolability of the work and result of execution are protected by the rules of Part IV of the Civil Code of the Russian Federation of the author or executor, regardless of providing legal protection of such results of intellectual activity at the time of their forming.
Copyright laws regulate the civil legal relations for using works of science, literature and art. Such relationships are formed as the result of the author’s writing his or her texts. In this case the author can rightfully claim copyright of the work.
The author has certain rights to reuse the work (see: “Ethical Aspects in Terms of Multifold Publications).
Licenses
All copyrights on the articles belong to their authors. The author transfers the rights on using the article the publisher.
PDF versions of scholarly articles of the journal PMN are published by using the license Attribution Non-Commercial No Derivatives cc by-nc-nd, allowing loading and distributing works on the assumption of indicating the authorship. The works may not be changed in any way or used for commercial interests.
Criteria for Authorship, Co-authorship
The term “author” refers to all persons (co-authors) who have made a substantial contribution to conducting the research and creation of the manuscript and responsible for its content. The person (author) who has submitted the manuscript to the editorial board shall bear responsibility for the complete list of the group of authors and the changes made to the manuscript in accordance with the results of the peer reviewing and editing.
1. Authorship is based on the following criteria:
1) The author made a substantial contribution to the research activity and development of concept, collected the data, made analysis and interpretation of the data.
2) The author carried out the writing of the text of draft articles and edited it attentively and substantially.
3) The author approved the final version of the article prior to its submission.
4) The author bears responsibility for the integrity of all parts of the manuscript.
2. The authors shall guarantee that the submitted manuscript is the original work.
3. Scholarly reviews for some issue or other should be objective, present material in a wide range and at the same time take into account the views of the author of the review.
4. The authorship of scholarly publications is obligated to reflect accurately the contribution of individuals to the research activity, with specific information about the authors.
5. The authors may not mislead the readers by publishing acknowledgements of gratitude to people who were not actually involved in writing the work. Other persons who made contribution to the work, but are nevertheless not the authors, may be listed in the rubric of “Acknowledgements,” with indications of the type and extent of their activities.
6. Authors are obligated to provide a description of their contribution to the publication.
7. The order of authorship must be a joint resolution of co-authors. The authors should be ready to explain the order of their enumeration and listing.
8. The authors shall be entirely responsible for the correct definition of authorship acting in accordance with the rules adopted in their institution.
9. Investigators must ensure that only those persons who meet the criteria for authorship (that made a significant contribution to the work), shall be considered the authors, and the researchers who do not merit authorship will be excluded from the list of authors.
References
2. Gorbunova I. B. Audiovizual'nyy sintez: istoriya, sovremennoe sostoyanie, perspektivnoe znachenie dlya muzykal'noy teorii i praktiki [Audiovisual Synthesis: History, Current Status, Promising Value for Music Theory and Practice]. Mir nauki, kul'tury, obrazovaniya [The World of Science, Culture, Education]. 2014. No. 6 (49), pp. 456–461.
3. Gorbunova I. B. Informatsionnye tekhnologii v muzyke: uchebnoe posobie dlya studentov vysshikh uchebnykh zavedeniy, obuchayushchikhsya po napravleniyu “Pedagogicheskoe obrazovanie”: v 4 t. [Information Technologies in Music: A Textbook for Students of Higher Educational Institutions Enrolled in the Direction of “Pedagogical Education”: in 4 Volumes]. St. Petersburg: Publ. house of the Herzen State Pedagogical University of Russia, 2009. Vol. 1: Arkhitektonika muzykal'nogo zvuka [Architectonics of Musical Sound]. 2009. 175 p.; Vol. 2: Muzykal'nye sintezatory [Music Synthesizers]. 2010. 215 p.; Vol. 3: Muzykal'nyy komp'yuter [Musical Computer]. 2011. 411 p.
4. Gorbunova I. B. Informatsionnye tekhnologii v muzyke i kompleksnaya model' eyo semanticheskogo prostranstva [Information Technologies in Music and Integrated Model of its Semantic Space]. Nauchno-tekhnicheskie vedomosti Sankt-Peterburgskogo gosudarstvennogo politekhnicheskogo universiteta. Gumanitarnye i obshchestvennye nauki [Scientific-Technical Bulletin of Saint-Petersburg State Polytechnic University. Humanities and Social Sciences]. 2014. No. 4 (208), pp. 152–161.
5. Gorbunova I. B. Komp'yuternye nauki i muzykal'no-komp'yuternye tekhnologii v obrazovanii [Computer Science and Music Computer Technologies in Education]. Teoriya i praktika obshchestvennogo razvitiya [Theory and Practice of Social Development]. 2015. No. 12, pp. 428–432.
6. Gorbunova I. B. Muzykal'noe programmirovanie, ili Programmirovanie muzyki i muzykal'no-komp'yuternye tekhnologii [Music Programming, or Musical Programming and Music Computer Technologies]. Teoriya i praktika obshchestvennogo razvitiya [Theory and Practice of Social Development]. 2015. No. 7, pp. 213–218.
7. Gorbunova I. B. The Role of Musical Computer Technologies in the Training of the Modern Music Teacher. Problemy muzykal'noj nauki/Music Scholarship. 2014. No. 3 (16), pp. 5–10. (In Russ.)
8. Gorbunova I. B. “Estetika: informatsionnyy podkhod” Yu. Ragsa: aktual'noe znachenie i perspektivy [“Aesthetics: Information Approach” by Yu. Rags: Relevance and Perspectives]. Teoriya i praktika obshchestvennogo razvitiya [Theory and Practice of Social Development]. 2015. No. 2, pp. 86–90.
9. Gorbunova I. B., Zalivadny M. S. Informatsionnye tekhnologii v muzyke: uchebnoe posobie dlya studentov vysshikh uchebnykh zavedeniy, obuchayushchikhsya po napravleniyu “Pedagogicheskoe obrazovanie”: v 4 t. [Information Technology in Music: A Textbook for Students of Higher Educational Institutions Enrolled in the Direction of “Pedagogical Education”: in 4 Volumes]. St. Petersburg: Publ. house of the Herzen State Pedagogical University of Russia, 2013. Vol. 4: Muzyka, matematika, informatika [Music, Mathematics, Computer Science]. 181 p.
10. Gorbunova I. B., Zalivadny M. S. Concerning Mathematical Methods in Music Research and Preparation of Musicians. Problemy muzykal'noj nauki/Music Scholarship. 2013. No. 1 (12), pp. 272–276. (In Russ.)
11. Gorbunova I. B., Zalivadny M. S. Opyt matematicheskogo predstavleniya muzykal'no-logicheskikh zakonomernostey v knige Ya. Ksenakisa “Formalizovannaya muzyka” [Experience of Mathematical Representation of Musical-Logical Regularities in the Book by I. Xenakis “Musiques formelles”]. Obshchestvo. Sreda. Razvitie [Society. Environment. Development]. 2012. No. 4 (25), pp. 135–139.
12. Gorbunova I. B., Zalivadny M. S., Kibitkina E. V. Muzykal'noe programmirovanie: uchebnoe posobie dlya studentov vysshikh uchebnykh zavedeniy, obuchayushchikhsya po napravleniyu 050100 – Pedagogicheskoe obrazovanie [Music Programming: A Textbook for Students of Higher Educational Institutions Enrolled in the Direction 050100 – Teacher Education]. St. Petersburg: Publ. house of the Herzen State Pedagogical University of Russia, 2012. 195 p.
13. Gorbunova I. B., Chibirev S. V. Komp'yuternoe modelirovanie protsessa muzykal'nogo tvorchestva [Computer Modeling of Creative Process in Music]. Izvestiya Rossiyskogo gosudarstvennogo pedagogicheskogo universiteta im. A. I. Gertsena [Proceedings of the Herzen State Pedagogical University of Russia]. 2014. No. 168, pp. 84–93.
14. Rags Yu. N. Akusticheskie znaniya v sisteme muzykal'nogo obrazovaniya [Acoustic Knowledge in the System of Music Education]. Ryazan: Litera M, 2010. 336 p.
15. Rags Yu. N. Perspektivy razvitiya kursa informatiki v muzykal'nykh obrazovatel'nykh uchrezhdeniyakh [Prospects of Development of Informatics Course in Music Educational Institutions]. Sovremennoe muzykal'noe obrazovanie – 2003: materialy II Mezhdunar. nauch.-prakt. konf. (9–11 oktyabrya 2003 g.) [Contemporary Music Education – 2003: Proceedings of the II International Scientific and Practical Conference]. Ed. by I. B. Gorbunova. St. Petersburg: Publ. house of the Herzen State Pedagogical University of Russia, 2003, pp. 200–203.
16. Shveytser A. Iogann Sebastyan Bakh [Schweitzer A. Johann Sebastian Bach]. Moscow: Klassika-XXI, 2011. 816 p.
17. Shubnikov A. V., Koptsik V. A. Simmetriya v nauke i iskusstve [Symmetry in Science and Art]. Moscow: Nauka, 2002. 429 p.
18. D’Erlanger R. La musique arabe, ses règles et leur histoire. T. 3: Safiyu-d-Din. Paris: Geuthner, 1938. 525 p.
19. Gorbunova I. B. Electronic Musical Instruments: to the Problem of Formation of Performance Mastery. 15th PARIS International Conference on Education, Economics, Humanities and Interdisciplinary Studies (EEHIS-18): Int'l Conference Proceedings. Budapest, 2018, pp. 23–28.
20. Gorbunova I. B. “New tool for a musician”. ICASET-18, ASBES-18, EEHIS-18. 16th International Conference on Literature, Languages, Humanities and Social Sciences (LLHSS-18): International Conference Proceedings. Paris, 2018, pp. 144–149.
21. Kurth E. Grundlagen des linearen Kontrapunkts. Berlin: Max Hesse, 1922. 532 p.
22. Lissa Z. O wielowarstwowości kultury muzycznej. Muzyka. 1959. No. 1, S. 3–22.
23. Lukács G. History and Class Consciousness. MIT Press: Print, 1971. 467 p.
24. Schillinger J. The Schillinger System of Musical Composition. Vol. 1–2. New York: Carl Fischer, 1946. 1640 p.
25. Xenakis I. Musiques formelles. La Revue musicale. Paris, 1963. No. 253/254. 232 p.