Jing Fang (, 78–37 BC), born Li Fang (), courtesy name Junming (), was born in present-day 東郡頓丘 ( Puyang, Henan) during the Han Dynasty (202 BC – 220 AD). He was a

Chinese Chinese can refer to: * Something related to China * Chinese people, people of Chinese nationality, citizenship, and/or ethnicity **''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation ** List of ethnic groups in China, people of va ...

music theorist, mathematician and

astrologer Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Dif ...

. Although better known for his work in musical measurements, he also accurately described the basic mechanics of

lunar Lunar most commonly means "of or relating to the Moon". Lunar may also refer to: Arts and entertainment * ''Lunar'' (series), a series of video games * "Lunar" (song), by David Guetta * "Lunar", a song by Priestess from the 2009 album ''Prior t ...

and solar eclipses.

Yijing

The historian

Ban Gu Ban Gu (AD32–92) was a Chinese historian, politician, and poet best known for his part in compiling the ''Book of Han'', the second of China's 24 dynastic histories. He also wrote a number of '' fu'', a major literary form, part prose ...

(32–92 AD) wrote that Jing Fang was an expert at making predictions from the

hexagrams , can be seen as a compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green). A hexagram ( Greek language, Greek) or sexagram (Latin) is a six-pointed ...

of the ancient ''

Yijing The ''I Ching'' or ''Yi Jing'' (, ), usually translated ''Book of Changes'' or ''Classic of Changes'', is an ancient Chinese divination text that is among the oldest of the Chinese classics. Originally a divination manual in the Western Zhou ...

''. A book on Yijing divination attributed to him describes the najia method of hexagram interpretation, which correlates their separate lines with

elements Element or elements may refer to: Science * Chemical element, a pure substance of one type of atom * Heating element, a device that generates heat by electrical resistance * Orbital elements, parameters required to identify a specific orbit of ...

of the

Chinese calendar The traditional Chinese calendar (also known as the Agricultural Calendar ��曆; 农历; ''Nónglì''; 'farming calendar' Former Calendar ��曆; 旧历; ''Jiùlì'' Traditional Calendar ��曆; 老历; ''Lǎolì'', is a lunisolar calendar ...

Music theory

According to the 3rd-century historian

Sima Biao Sima Biao (; between 238 and 246 – 306), style name Shaotong (), was an historian and nobleman during the Jin dynasty of China. Biography Sima Biao was the eldest son of Sima Mu (司馬睦), Prince of Gaoyang. His grandfather was Sima Ji ...

, Jing Fang received an appointment as an official in the Music Bureau under Emperor Yuan of Han (r. 48–33 BC).McClain and Ming, 208. Jing Fang was the first to notice how closely a succession of 53

just fifth In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval from the first to the last of five ...

s approximates 31

octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

s. 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^ = 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.McClain and Ming, 212. 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 Sunlight is a portion of the electromagnetic radiation given off by the Sun, in particular infrared, visible, and ultraviolet light. On Earth, sunlight is scattered and filtered through Earth's atmosphere, and is obvious as daylight when t ...

. 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 Zhang Heng (; AD 78–139), formerly romanized as Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty. Educated in the capital cities of Luoyang and Chang'an, he achieved success as an astronomer, ma ...

(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.

Notes

References