The Integrative Model for the Semantic Space of Music: Perspectives of Unifying Musicology and Musical Education

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.