Jing Fang (Chinese: ; pinyin: ; Wade-Giles: Ching Fang, 78–37 BC), born Li Fang (), courtesy name Junming (), was born in present-day ? (Puyang, Henan) during the Han Dynasty (202 BC – 220 AD). He was a Chinese music theorist, mathematician and astrologer. Although better known for his work in musical measurements, he also accurately described the basic mechanics of lunar and solar eclipses.
The historian Ban Gu (32–92 AD) wrote that Jing Fang was an expert at making predictions from the hexagrams of the ancient Yijing. A book on Yijing divination attributed to him describes the najia method of hexagram interpretation, which correlates their separate lines with elements of the Chinese calendar.
Jing Fang was the first to notice how closely a succession of 53 just fifths approximates 31 octaves. He came upon this observation after learning to calculate the pythagorean comma between 12 fifths and 7 octaves (this had been published ca. 122 BC in the Huainanzi, a book is written for the prince of Huainan), 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.
He accomplished this calculation by beginning with a suitable large starting value () 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. Instead, by rounding to about 6 digits, his calculations are within 0.0145 cents 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 --.
He was also an advocate of the theory that the light emanating from the spherical Moon (as seen from Earth) was merely a reflection of sunlight. 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 philosopher Wang Chong (27–97 AD), yet embraced by the mathematician, inventor, and scientist Zhang Heng (78–139 AD).
Jing Fang stated:
The moon and the planets are Yin; 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.
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.