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Zhu Zaiyu

Ming Dynasty Prince and Pioneer of Equal Temperament

Zhu Zaiyu (1536–1611), a Ming dynasty prince and polymath, made groundbreaking contributions at the nexus of mathematics, physics, and music theory. He is most renowned for accurately calculating the equal temperament musical tuning system using rigorous mathematical methods.

Before Zhu’s work, musical scales were based on imperfect ratios. In 1584, he mathematically derived a tuning where an octave is divided into 12 equal semitones, each with frequency ratio: \[ \sqrt{2} \] He refined this through continued fraction approximations to enormous precision. His treatises—including Lü Xue Xin Shuo and Suan Xue Xin Shuo—provided exact specifications and proofs of equal temperament, an achievement unmatched in acoustic history.

Zhu combined his mathematical precision with astronomical and calendrical scholarship. He accurately calculated the length of the tropical year and corrected the Ming calendar, and described magnetic declination near Beijing. These calculations relied on mathematical astronomy and numerical analysis.

His interdisciplinary brilliance—blending number theory, physics, music, and astronomy—represents a rare harmony of quantitative artistry and scientific method. Zhu Zaiyu is honored both as a scholar of tone and as a rigorous mathematician, embodying the unity of art and science during the Ming dynasty.