Research And Practice Of David Levin's Theory Of Generalized Tonal Functions

David Lewin(1933-2003),an American music theorist,built the Generalized Interval Systems(GIS)and Transformation Networks on the basis of set theory and group theory.In the formalization process of generalized interval and transformation theory,he also formalized the Generalized Theory of Tonal Functions.The Generalized Theory of Tonal Functions is based on the traditional Riemann System theory of harmony function,and generalizes the traditional tonality and chord function.After the construction of Riemann System(RS),a new RS associated with Riemann System is obtained by different operation modes.This paper mainly includes three parts.The first part is an overview of David Levin's Generalized Theory of Tonal Functions.This part first interprets the structure of chords;secondly,constructs RS according to chords;lastly,seven operation modes of RS;moreover,seven different operations are classified according to the specific operation modes.The second part is to analyze the two works created by using the Generalized Theory of Tonal Functions.Among them,Academic Festival Overture is the first time to use this theory,which has experimental and exploratory significance;relatively speaking,the operation used in the creation of third movement of Piano Trio,Dawn and the transformation of RS become complex.In order to illustrate the practical significance of the application of the theory.The third part is the enlightenment of Generalized Theory of Tonal Functions.The concepts of tonality and function of harmony mentioned in the theory originate from tradition.However,the generalization of tonality and chord function is a mathematical reflection of traditional modernity.In addition,there are superimposed chords which are not mentioned in the theory,the reconstruction of different cardinal scales and the ordering of scale sets,which can be used as further extensions of the theory.Finally,through the combination of theory and practice,the construction concept of the theory and the concept of music creation are explained.