On the Approaches to the "Neorimanian Theory": David Lewin’s Transformational Approach
Authors: Ustyuzhanina Nadiia 
Published: December 2023

Today, Ukrainian musicology is opening up to the world, testifying to its bright potential, prospects and opportunities for cooperation with the international scientific environment. Along with the demonstration of one's own achievements, it is necessary to master the methods of analysis common and used today in North American and European musicology.
A wide panorama of modern approaches demonstrates significant potential for studying the pitch parameter in the music of the 20th–21st centuries. Among the basic approaches (Schenkerian reduction, Babbitt-Forte’s set theory), the neo-Riemannian method of analysis of triadic pitch structures, characteristic of North American musicology, is of great interest to Ukrainian scientists. The mastery of this method causes certain difficulties, connected with its basing mainly on the neopositivist methodology and the use of various mathematical procedures related to the processes of transformation of sound objects — in this case, triadic pitch structures. The lack of investigation of this problem in Ukrainian musicology determines the relevance of the study.
The purpose of the article is to highlight the history of the development of the NeoRiemannian approach to the analysis of pitch structures in the research of one of its first developers, David Lewin, and the general characteristics of a number of analytical techniques.
Immersion in North American music theory and mastering the toolkit of neopositivist methods allows you to get closer to understanding the specifics of various modern analytical approaches that develop at the intersection with mathematical theories. Among the steps we have taken in this mastering, in particular, the presentation of the Neo-Riemannian operations and the introduction into the scientific circulation of the works of North American musicologists.
The methodological basis of the article is the method of structural analysis and a special neo-Riemannian method of analysis of pitch structures.
The results and conclusions. A general introduction to the history of the emergence of the Neo-Riemannian theory and its main provisions in the works of the first Neo-Riemannian researcher D. Lewin (in particular, the transformational attitude, triadic transformation, graphs, networks) made it possible to form an idea of one of the methods of pitch analysis common in North American musicology in musical works. Representing one of the leading branches of modern music theory, which began to take shape in the 1950–1960s, the neo-Riemannian concept received further development in the works of R. Cohn, J. Hook, J. N. Straus, F. Lehman and is still at the stage of development of ideas based on the philosophy of neopositivism.
All partially demonstrated techniques of the NR method can be applied during the analysis of triadic structures both in tonal music and in works where the functional relationship between triads doesn’t work. Such an opportunity to test the method on musical samples of different times and styles is considered interesting and relevant. An attempt to outline only the main provisions of the neo-Riemannian theory prompts a more detailed consideration of its ideas in connection with related concepts, which also involve mathematical means of sound material analysis (in particular, D. Tymoczko’s chordal geometry, Klumpenhouwer networks). In addition, the research of the very direction of neopositivism in music theory, which needs a thorough study, seems promising.