The prince's mathematics and acoustics: an examination of the sources of Zhu Zaiyu's innovation in musical temperament and his mathematical approach (Q6579268)

This paper aims to reconstruct Zhu Zaiyu's (1536--1611) mathematical knowledge in his work on equal temperament. Zhu used geometric ratios instead of fractional proportions to divide the musical scale resulting in the equal-tempered scale. The article focuses on the classical sources of Zhu Zaiyu's ideas in creating a new temperament and the sources of his mathematical deductions. It provides rectifications to the interpretation, in particular the concept of \textit{lü}, of Zhu Zaiyu's texts by the contemporary Chinese historian of acoustics Xu Fei 徐飞, providing a more detailed and contextualised translation of the relevant primary texts.