A form of invisibility? Did Western equal-tempered music-math originate in China? Math Dr. George Gheverghese Joseph

We get this 10 mn overview of his argument. youtube vid

His argument is summed up here:

As one example, Joseph cited recent research (still in progress) demonstrating that a Chinese mathematician, Zhu Zaiyu (1536–1611), discovered a mathematical method involving the twelfth root of 2 to create an equal-tempered 12-tone musical scale (dividing an octave into twelve equal semitones) no later than 1581. Simon Stevin (1548–1620), who is often credited with the discovery, provided hints of his method only as early as 1585. Marin Mersenne (1588–1648) wrote about equal temperament in his 1637 book Harmonie universelle, possibly after seeing Stevin's work.
But establishing priority isn't enough, Joseph said. "Could this knowledge have been transmitted from China to the West?" he asked.
Joseph and a colleague are now searching for evidence suggesting that transmission of the necessary knowledge could have occurred via the Jesuits in a chain from Zhu Zaiyu to Jesuit scholar Matteo Ricci (1552­–1610), who worked in China, to Jesuit mathematician Christopher Clavius (1538–1612) to Niklaas Trigault (1577–1628) to Stevin and Mersenne.

His whole lecture is here -

 This pdf link is Dr. Joseph's article on square root solutions that are non-western



 


 and

According to Gene Cho, Zhu Zaiyu was the first person to solve the equal temperament problem mathematically.^[16] Matteo Ricci, a Jesuit in China, was at Chinese trade fair in Canton the year Zhu published his solution, and very likely brought it back to the West.^[17] Murray Barbour said, "The first known appearance in print of the correct figures for equal temperament was in China, where Prince Tsaiyü's brilliant solution remains an enigma."^[18] The 19th-century German physicist Hermann von Helmholtz wrote in On the Sensations of Tone that a Chinese prince (see below) introduced a scale of seven notes, and that the division of the octave into twelve semitones was discovered in China.^[19]
Zhu Zaiyu illustrated his equal temperament theory by construction of a set of 36 bamboo tuning pipes ranging in 3 octaves, with instructions of the type of bamboo, color of paint, and detailed specification on their length and inner and outer diameters. He also constructed a 12-string tuning instrument, with a set of tuning pitch pipes hidden inside its bottom cavity. In 1890, Victor-Charles Mahillon, curator of the Conservatoire museum in Brussels, duplicated a set of pitch pipes according to Zhu Zaiyu's specification. He said that the Chinese theory of tones knew more about the diameter of pitch pipes than its Western counterpart, and that the set of pipes duplicated according to the Zaiyu data proved the accuracy of this theory.^[20]

 But another scholar disagrees:

According to Fritz A. Kuttner, a critic of the theory,^[2] it is known that "Chu-Tsaiyu presented a highly precise, simple and ingenious method for arithmetic calculation of equal temperament mono-chords in 1584" and that "Simon Stevin offered a mathematical definition of equal temperament plus a somewhat less precise computation of the corresponding numerical values in 1585 or later." The developments occurred independently.^[3]

 

 pdf link

And so Kuttner reviews the development of equal-tempered tuning going back to the mean proportional math of Archtyas. 

One of the problems I noticed with Dr. Joseph's argument is he misrepresents the Chinese ancient music tuning system. He says it is based on planetary or astronomical cycles and in particular the 12 months of the year. This implies it is a solar based tuning but actually the tuning is lunar based.



So Kuttner details how the Western academics projected a "square root" procedure when in actuality there had been a slight modification of the traditional Perfect Fifth (2/3 as yang) and Perfect fourth (3/4 as yin) tuning.




So the 81 is based on the lunar calendar to attempt a synchronization with the solar calendar with the lunar calendar as the starting note - due to Daoist alchemical reasons!




So contrary to the popular "meme" that equal-tempered tuning was invented in  China, based on the square root of two, this simply is not true! As Dr. Joseph admits he doesn't really know much about music theory. Nevertheless his speculative claim about the Jesuits is fascinating. Still the music theory origin of Western mathematics is even more fascinating, as math professor Luigi Borzacchini has detailed.

And yet I prefer the Daoist tuning and so was glad to have gleaned another analysis (even if it mirrored the Western equal-tempered tuning). As Dr. Patrick E. Moran (prof. emeritus) noted - this supposed equal-tempered tuning was not used in China, at least not for long.