The "Common Pitch-class Vector" Of Pitch-class Set And The "Similarity Relationship(S-type)" Inside The Set Class

I expand the theory of "similarity relationship" in Allen Forte’s "pitch-class set theory".According to "similarity relationship within the same set class",which is not involved in "similarity relationship",the concepts of "pitch-class similarity S-type relationship" and "common pitch-class vector" are put forward.And through the research of the pitch organization technique and the pitch-class similarity S-type relationship in several works,this theory is proved to a certain extent.This paper is mainly divided into three chapters,which are "pitch-class similarity S-type relationship and common pitch-class vector","S-type relationship in the part" and "S-type relationship in the whole".The first chapter mainly introduces the main content and views of the theory,and the last two chapters are based on the actual music works,with a number of music fragments to explain the use of "pitch-class similarity S-type relationship" and the main characteristics.Two complete works of different composers,different genres,and different pitch materials are used to demonstrate the analytical efficiency and application range of the "pitch-class similarity S-type relationship".Small to local,large to the whole,and strive to show the practicability and applicability of the analysis method in multi-latitude,multi-perspective and multi-level.Through the expansion of the similarity relationship,the analyst can observe the intimacy between different forms of the same set,which provides a theoretical basis and enriches the analysis and observation latitude of the pitch-class set.At the same time,it provides a theoretical reference for the creators when choosing the form of layout of the same set in their works.The analysis results also show that the "pitch-class similarity S-type relationship" is more suitable for observing those works which are more concentrated in the use of sets.Of course,for the works with richer pitch materials and more diverse sets,it can also reflect the corresponding analysis efficiency.