Mathematical System and Understanding Model of"Five Scales"
The adjustment and identification of the order of"Five Scales"(Gong,Shang,Jue,Zhi,Yu)re-poses the debugging and formation of the"number 5-10-12"model,which not only establishes the mathematical system of"Five Scales"but also indicates the process to expand music knowledge in early China.The profit after loss and the loss after profit of the trisect profit and loss method respectively identify the pitch order(middle Gong scale and lead Gong scale)of Five Scales.Establishment of numerical values and arrangement of numerical magni-tudes of the Five Scales are all headed by Gong scale.With Gong scale as the center,the"number 5-10-12"mod-el is formed in the system of monthly order.The model constitutes not only an equal division structure mathemati-cally but also the balance effect in argumentation,which lays the foundation for"use of mathematical methods for analysis"in early China.
Five Scalessuccessive promotion and successive restriction of the Five Elements"number 5-10-12"Yueji(Book of Music)Yuewei(Book of Music Divination)
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