Yijing

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.

Music theory

According to the 3rd-century historian Sima Biao, Jing Fang received an appointment as an official in the Music Bureau under Emperor Yuan of Han (r. 48–33 BC).

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 (3^{11} = 177147) that could be divided by three easily, and proceeded to calculate the relative values of successive tones by the following method:

• Divide the value by three. 177147/3 = 59049

• Add this value to the original. 177147 + 59049 = 236196

• The new value is now equal to 4/3 of the original, or a perfect fourth, which is equivalent to a perfect fifth inverted at the octave. (Alternatively, he would subtract 1/3 from the interval, equivalent to a perfect fifth down, to keep all of the values greater than 177147, or less than 354294, it's double, effectively transposing them all into the range of a single octave.)

• Proceed now from this new value to generate the next tone; repeat until all tones have been generated.

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

—177147 / 176776.

This value would later be calculated precisely by Nicholas Mercator in the 17th century (see: history of 53 equal temperaments).

Astronomy

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:

Death

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.

生平

本姓李，因其愛好吹奏音律，自定為京氏，羌笛原本有三個音孔，京房改進後成了多一個，音孔定為商聲，從而使它能奏全宮、商、角、徵、羽五聲。

漢元帝時為郎、魏郡太守。治易學，師從梁人焦延壽，詳於災異，開創了京氏易學，有《京氏易傳》存世。《漢書》有傳。焦延壽曾憂慮說：「得我道以亡身者，京生也。」

生平

漢元帝初元四年（前45年），西羌叛亂，又有日蝕。漢元帝召見他時，京房宣稱：「古帝王以功舉賢，則萬化成，瑞應著；末世以毀譽取人，故功業廢而致災異。宜令百官各試其功，災異可息。」又提出《考功課吏法》。當時宦官石顯擔任中書令，誣陷其誹謗朝政，歸惡天子，元帝將京房下獄，死獄中。

易學流派

《京氏易傳》

;著作

:《京氏易傳》

;作者

:京房 (魏郡太守)

;爭議

:根據江弘遠《京房易學流變考》一書，自從《京氏易傳》出現後，受朱熹、惠棟，以及《四庫總目提要》的推波助瀾，均認為此書及其條例是出自京房本人之手。本書以沈延國論點加以延伸，確定京房是以所統領的六十卦反復配六十鐘律，八宮卦、納甲、納音則是由荀爽、虞翻、幹寶等另一非京氏易學流派演變而來，從《京氏易傳》出現後，遂取代京房原有的模式。

;八宮六十四卦

:京房易；京氏易；八宮卦

參考書目

• 《漢書·京房傳》

注釋