Solved Correctly, Adopted by No OneZhu Zaiyu and Equal Temperament · 1584, Henan
1584Ming ChinaKenneth Robinson 1980In imperial China, pitch was not a musical question but a metrological one. The Han shu treatise on pitch-pipes and the calendar records the huangzhong pipe as nine cun long and holding 1,200 millet grains — a pitch standard that doubled as the standard of length and volume, the doctrine of "one pitch system, one system of weights and measures." Liu Xin cast official measures on this basis under Wang Mang; the resulting bronze jar survives in Taipei. Hence every dynastic change began by "rectifying the pitch pipes": get the pitch wrong and the foot-rule is wrong too.
The trouble lay in how pitches were generated. The san-fen sun-yi method (successive perfect fifths) does not close after twelve steps; it overshoots by about 23.5 cents — what Europe calls the Pythagorean comma. The standard remedy was to add more pitches: Jing Fang's sixty, Qian Yuezhi's three hundred and sixty. Push the error downstream, never confront it.
Zhu Zaiyu (1536–1611), son of the Prince of Zheng, spent nineteen years living alone in an earthen hut outside the palace gate after his father was stripped of rank, reading and calculating. His New Account of the Science of the Pitch-Pipes (1584) gave the "new density ratio": pipe lengths in a geometric series with a common ratio of the twelfth root of two. Working an eighty-one-column abacus through repeated square and cube roots, he reached 1.059463094359295264561825 — twenty-five significant figures, the first exact solution of twelve-tone equal temperament anywhere, half a century before Mersenne's 1636 account. He presented the work to the Wanli emperor in 1606. The Ministry of Rites deliberated and did nothing.
Suppose the court had adopted it. Most likely nothing would have changed musically — the binding constraint was elsewhere. Equal temperament took hold in Europe because hardware forced it: a harpsichord has twelve keys per octave, modulation inevitably goes sour, and a tuner had to decide daily which key would sound worst. The pain settled every day. China's lead instruments — qin, dizi, sheng — are retuned per piece; no one was hurting on a daily cycle. Zhu solved the Ministry's problem; Europe solved the keyboard's. A ministry can defer; a keyboard cannot. The live dispute is transmission: Needham suspected the method travelled west via missionaries to Mersenne, but there is no direct evidence, and most scholars now read the two as independent discoveries.
Someone on the team writes up the right design, but no role in the organization is hurt by the problem every day — so the design stays in the doc. Standards fights are rarely won on correctness; they are won on whose pain is sharper.