Jing Fang (京房) (78–37 BC),[a] bornLi Fang (李房),courtesy nameJunming (君明), was aChinesemusic theorist,[1]mathematician andastronomer born in present-dayPuyang, Henan[b][citation needed] during theHan dynasty (202 BC – 220 AD). Although better known for his work in musical measurements, he also accurately described the basic mechanics oflunar and solar eclipses.
The historianBan Gu (32–92 AD) wrote that Jing Fang was an expert at making predictions from thehexagrams of the ancientYijing.[2] A book onYijing divination attributed to him describes thenajia method of hexagram interpretation, which correlates their separate lines withelements of theChinese calendar.[3] Not only was he instrumental in the development of Yijing correlative cosmology, but he has also shed a new light on China's history, in particular Qin and Han.[4]
According to the 3rd-century historianSima Biao, Jing Fang received an appointment as an official in theMusic Bureau underEmperor Yuan of Han (r. 48–33 BC).[2]
Jing Fang was the first to notice how closely a succession of 53just fifths approximates 31octaves. He came upon this observation after learning to calculate thepythagorean comma between 12 fifths and 7 octaves,[5] and extended this method fivefold to a scale composed of 60 fifths, finding that after 53 new values became incredibly close to tones already calculated. The pythagorean comma had been published ca. 122 BC in theHuainanzi, a book is written forthe prince ofHuainan. Huainanzi emphasizes that the number of musical temperament and calendar reflect the path of heaven and earth.[6]
He accomplished this calculation by beginning with a suitable large starting value ()[7] that could be divided by three easily, and proceeded to calculate the relative values of successive tones by the following method:
To produce an exact calculation, some 26 digits of accuracy would have been required.[8] Instead, by rounding to about 6 digits, his calculations are within 0.0145cents of exactness, which is a difference much finer than is usually perceptible. The final value he gave for the ratio between this 53rd fifth and the original was —.[8][9]
This value would later be calculated precisely byNicholas Mercator in the 17th century (see:history of 53 equal temperaments).
He was also an advocate of the theory that the light emanating from the sphericalMoon (as seen fromEarth) wasmerely a reflection ofsunlight. This was known as the 'radiating influence' theory in ancient China, which stated that the light of the Moon was merely the light reflected from the Sun and that the celestial bodies were spherical. This accurate theory was dismissed by the philosopherWang Chong (27–97 AD), yet embraced by the mathematician, inventor, and scientistZhang Heng (78–139 AD).
Jing Fang stated:
The moon and the planets areYin; they have shape but no light. This they receive only when the sun illuminates them. The former masters regarded the sun as round like a crossbow bullet, and they thought the moon had the nature of a mirror. Some of them recognized the moon as a ball too. Those parts of the moon which the sun illuminates look bright, those parts which it does not, remain dark.[10]
It is recorded that he was executed by beheading in the marketplace in 37 BC under the Emperor's orders after he allegedly slung false accusations at a high official for infringing upon the law.[2]
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