A Study On The Creation Of Zhu Zai - Yu And Stevin

As the most widely used temperament system, twelve-tone equal temperament theory shows an instance of the artistic practice concreted with the mathematical calculation in the history of mathematics and temperament theory. It plays an important role in the history of temperament theory in both China and West and lays a mathematical foundation of the adjustment of modern keyboard instruments so as to make the piano, which is called as the king of musical instruments. The first derivation of12-tone equal temperament was achieved in1584by Zhu Zaiyii,(1536—1611), a prolific scholar and prince associated with the Ming court. A little more than twenty years later, in his1606manuscript titled "Van de Spoegheling der Singconst",the Dutch mathematician Simon Stevin (1548—1620), performed a similar derivation. Both Zhu and Stevin’s equal temperament theory have enriched the basic system of temperament theory and practice, and both have made immeasurable contribution to the progress of human civilization and advancement of science and culture. In this paper, we discuss their creative processes and analysis the different realistic foundations between them so as to reveal the different intentions, processes and scientific traditions, which reveal close links between arithmetic, geometry, and the theory of musical temperament in both cultures during the period.Based on the existing research work, this paper focuses on the research of temperament and its influence on mathematical calculation, meanwhile, it takes "why mathematical?" as its methodological guide, this paper will use the following methods:investigation into the original literature, combination of the internal and external historical view; in the whole and comprehensiveness principle, to make the multi-faced, multi-perspective study of the elements relevant to understanding and grasping the equal temperament theory; combining quantitative analysis with qualitative analysis, the basic theory of music is the basis and prerequisite of temperament theory while the calculating system is the development and extension of the theory of music; both cross-sectional and longitudinal research, with the development of temperament theory, to analysis the equal temperament constitute a vertical historical and horizontal developmental process and the transitional processes, to perform a comprehensive analysis of the impact factors and the heritage relationship; with a combination of microscopic view and macroscopic view, to analysis the communication and integration of different disciplines related to equal temperament theory and pay attention to the details. The chief achievements are as follows:1. Established the foundations of comparative study of equal temperament between Zhu Zaiyu and Stevin:being with the brief history of the temperament theory in China and West and introduce the multiple disciplines, such as physical acoustics, psychology and vocal techniques; through the quantitative process of the sensations of tone to construct united system of psychology and vocal techniques, physical acoustics and mathematical calculation between the development of temperament theory of China and West; unifying the related concepts and notations.2. On the basis of the existing research of Zhu Zaiyii’s equal temperament to analysis the history of Chinese temperament start with San fen sun yi method. It is by all means not a coincidence that twelve-tone equal temperament was first created in China, combining many remarkable achievements of Chinese history of science and technology and reflecting the rigorous attitude of Zhu Zaiyii, as well as the solid theoretical base of Chinese traditional science. Zhu Zaiyu’s Lii xue xin shuo, Lu lu jing yi, Suan xue xin shuo etc. which described the creation process of twelve-tone equal temperament and revealed close links between geometry, arithmetic, temperament and physical acoustics. This article analyzes the above factors to prove that the process of creating twelve-tone equal temperament embodied profound thinking about mathematical analysis, which was the fundamental base for Zhu Zaiyu’s work and was used consistently during the whole process of creating ’Xin fa mi lu’3. This paper tries to analyze the calculating processes of twelve-tone equal temperament by Simon Stevin, point out how to the mathematics method was firstly used to explore the rules of the equal temperament theory in the West. Through the restoration research of the calculating processes by Simon Stevin present the combination of axiomatic method and temperament theory by Stevin clearly and to supplement the research in this area. Meanwhile we make an objective evaluation on Stevin’s pioneering work under the research of history of mathematics and temperament theory. Stevin is a productive mathematician and engineer circa1600, his work on equal temperament fully embody the highest achievement.4. Perform a comparison of the historical and cultural background and motivation between Zhu and Stevin, meanwhile it includes the quantitative comparison of the beginning, procedure and accurate of the calculation of equal temperament theory.5. Dissect the application and evaluation of Zhu and Stevin’s equal temperament theory, which drew inspiration and provide referrals to the deep understanding of the complete picture of scientific development between China and West.