Jing Fang (, 78–37 BC), born Li Fang (),

courtesy name A courtesy name (), also known as a style name, is a name bestowed upon one at adulthood in addition to one's given name. This practice is a tradition in the East Asian cultural sphere, including China, Japan, Korea, and Vietnam.Ulrich Theo ...

Junming (), was born in present-day 東郡頓丘 ( Puyang, Henan) during the

Han Dynasty The Han dynasty (, ; ) was an Dynasties in Chinese history, imperial dynasty of China (202 BC – 9 AD, 25–220 AD), established by Emperor Gaozu of Han, Liu Bang (Emperor Gao) and ruled by the House of Liu. The dynasty was preceded by th ...

(202 BC – 220 AD). He was a Chinese

music theorist Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the " rudiments", that are needed to understand music notation ( ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

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. Di ...

. 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-pointe ...

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 Zho ...

''. 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 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, Jing Fang received an appointment as an official in the

Music Bureau The Music Bureau (Traditional Chinese: 樂府; Simplified Chinese: 乐府; Hanyu Pinyin: ''yuèfǔ'', and sometimes known as the "Imperial Music Bureau") served in the capacity of an organ of various imperial government bureaucracies of China: di ...

under

Emperor Yuan of Han Emperor Yuan of Han (Liu Shi 劉奭; 75 BC – 8 July 33 BC) was an emperor of the Chinese Han dynasty. He reigned from 48 BC to 33 BC. Emperor Yuan promoted Confucianism as the official creed of the Chinese government. He appointed Confucius ...

(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 ''The Prince'' ( it, Il Principe ; la, De Principatibus) is a 16th-century political treatise written by Italian diplomat and political theorist Niccolò Machiavelli as an instruction guide for new princes and royals. The general theme of ''The ...

Huainan Huainan () is a prefecture-level city with 3,033,528 inhabitants as of the 2020 census in north-central Anhui province, China. It is named for the Han-era Principality of Huainan. It borders the provincial capital of Hefei to the south, Lu'an ...

), 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 A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to ...

, 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 Nicholas (Nikolaus) Mercator (c. 1620, Holstein – 1687, Versailles), also known by his German name Kauffmann, was a 17th-century mathematician. He was born in Eutin, Schleswig-Holstein, Germany and educated at Rostock and Leyden after which h ...

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 The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

(as seen from

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...

) 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 ...

. 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, mat ...

(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

* Huang, Xiangpeng
"Jing Fang"
''

Encyclopedia of China The ''Encyclopedia of China'' () is the first large-entry modern encyclopedia in the Chinese language. The compilation began in 1978. Published by the Encyclopedia of China Publishing House, the encyclopedia was issued one volume at a time, begin ...