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

courtesy name A courtesy name ( zh, s=字, p=zì, l=character), also known as a style name, is an additional name bestowed upon individuals at adulthood, complementing their given name. This tradition is prevalent in the East Asian cultural sphere, particula ...

Junming (), was a Chinese

music theorist Music theory is the study of theoretical frameworks for understanding 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 ...

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, mathematical structure, structure, space, Mathematica ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

born in present-day Puyang, Henan during the

Han dynasty The Han dynasty was an Dynasties of China, imperial dynasty of China (202 BC9 AD, 25–220 AD) established by Liu Bang and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–206 BC ...

(202 BC – 220 AD). Although better known for his work in musical measurements, he also accurately described the basic mechanics of lunar and solar eclipses.

Yijing

The historian

Ban Gu Ban Gu (AD32–92) was a Chinese historian, poet, and politician 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 polygon, 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 l ...

of the ancient ''

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

''. 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, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...

. 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.

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 character, Traditional Chinese: 樂府; Simplified Chinese character, Simplified Chinese: 乐府; Pinyin, Hanyu Pinyin: ''yuèfǔ'', and sometimes known as the "Imperial Music Bureau") served in the capacity o ...

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 fifths approximates 31

octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...

s. He came upon this observation after learning to calculate the pythagorean comma between 12 fifths and 7 octaves, 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 the ''

Huainanzi The ''Huainanzi'' is an ancient Chinese text made up of essays from scholarly debates held at the court of Liu An, Prince of Huainan, before 139 BCE. Compiled as a handbook for an enlightened sovereign and his court, the work attempts to defi ...

'', a book is written for

the prince ''The Prince'' ( ; ) is a 16th-century political treatise written by the Italian diplomat, philosopher, and Political philosophy, political theorist Niccolò Machiavelli in the form of a realistic instruction guide for new Prince#Prince as gener ...

of Huainan. Huainanzi emphasizes that the number of musical temperament and calendar reflect the path of heaven and earth. 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 interval (music), 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 int ...

, 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 The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

(as seen from

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

) was merely a reflection of

sunlight Sunlight is the portion of the electromagnetic radiation which is emitted by the Sun (i.e. solar radiation) and received by the Earth, in particular the visible spectrum, visible light perceptible to the human eye as well as invisible infrare ...

. 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 romanization of Chinese, romanized Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty#Eastern Han (25–220 AD), Eastern Han dynasty. Educated in the capital citi ...

(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, be ...

'' (Music and Dance Edition), 1st ed. * McClain, Ernest and Ming Shui Hung. "Chinese Cyclic Tunings in Late Antiquity," ''Ethnomusicology'', Vol. 23, No. 2 (1979): 205–224. *Needham, Joseph (1986). ''Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth''. Taipei: Caves Books, Ltd. * Complete table of Jing Fang's hexagram values
Jing Fang Hexagram Table
(obsolete) * Comparing Jing Fang's and other hexagram sequences

* Matthews, William. ''Cosmic Coherence a Cognitive Anthropology through Chinese Divination''. Berghahn, 2022. * LI, XIFAN. ''General History of Chinese Art: From the Qin Dynasty to the Northern and Southern Dynasties''. DE GRUYTER, 2022. {{DEFAULTSORT:Jing, Fang Chinese music theorists 1st-century BC Chinese astronomers Chinese astronomers Mathematicians from Imperial China 1st-century BC Chinese philosophers 78 BC births 37 BC deaths Executed Han dynasty people Han dynasty musicians Han dynasty government officials People executed by the Han dynasty by decapitation Politicians from Puyang Executed people from Henan Political office-holders in Hebei Musicians from Henan Mathematicians from Henan 1st-century BC executions Ancient astronomers I Ching 1st-century BC mathematicians 1st-century BC musicians

Yijing

Music theory

Astronomy

Death

See also

Notes

References