Twelve-tone equal temperament: Prince Zhu Zhaiyu---his discovery and inspiration

The aim of this dissertation is to present a study on Prince Zhu Zhaiyu's inspiration on the discovery of twelve-tone equal temperament. Rather than exploring the mathematical details of the formulae that have been presented by several Chinese scholars, this research focuses on translating an excerpt of Lu and Shadow in his monumental work Lu Li Rong Tong (The Concordance Between the Ritual Tone System and Calendar, 1567), for indicating how Prince Zhu coined the three "pillars" of the equal temperament theory: equidistant semitone, equivalent enharmonic tones and exact return of the tonic pitch to the original position. Observing the amazing inter-relationship among ancient Chinese astronomy, calendrical science and tonal systems, Prince Zhu set up the flawlessly striking theory to calculate, with the aid of nine abacuses, the twelfth root of two for determining the discrete exact value up to the twenty-fourth decimal place (1.059463094359295264561825) of tempering each semitone prior to his contemporaries in the world.;This study also discusses misconceptions of the discovery in equal temperament: recognition of Ling Lun in 2550 B.C. as the first discoverer, Simon Stevin in the late sixteenth century and Marin Mersenne in the mid-seventeenth century. Moreover, this writing provides a synopsis of shortcomings of major tuning systems in the West (Pythagorean Tuning, Just Intonation and Meantone Temperament) and China (the historic and authoritative system---Sanfen Sunyi-fa , adding and subtracting of one-third method). Finally, this paper concludes with Prince Zhu's discovery on the incomparable tempering system of equal semitones to solve a few thousand years of temperament riddle: the failure to freely modulate and return to the original tonic. His significant contribution has been nominated as the fifth great ancient civilized invention in China and has become the standard Western temperament today.